LMFDB - Embedded newform 430.2.l.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(7,430)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("430.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	430.7
Dual form			430.2.l.a.123.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.547703 + 2.04406i) q^{3} -1.00000i q^{4} +(2.11862 - 0.715150i) q^{5} +(-1.05808 - 1.83265i) q^{6} +(-0.838501 - 3.12933i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.28011 - 0.739071i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.547703 + 2.04406i) q^{3} -1.00000i q^{4} +(2.11862 - 0.715150i) q^{5} +(-1.05808 - 1.83265i) q^{6} +(-0.838501 - 3.12933i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.28011 - 0.739071i) q^{9} +(-0.992405 + 2.00378i) q^{10} +5.57301 q^{11} +(2.04406 + 0.547703i) q^{12} +(-1.57463 - 5.87660i) q^{13} +(2.80568 + 1.61986i) q^{14} +(0.301431 + 4.72227i) q^{15} -1.00000 q^{16} +(5.34691 - 1.43270i) q^{17} +(1.42778 - 0.382571i) q^{18} +(-1.13275 - 1.96198i) q^{19} +(-0.715150 - 2.11862i) q^{20} +6.85577 q^{21} +(-3.94071 + 3.94071i) q^{22} +(-5.62275 - 1.50661i) q^{23} +(-1.83265 + 1.05808i) q^{24} +(3.97712 - 3.03027i) q^{25} +(5.26882 + 3.04195i) q^{26} +(-2.27724 + 2.27724i) q^{27} +(-3.12933 + 0.838501i) q^{28} +(-1.94032 + 3.36073i) q^{29} +(-3.55229 - 3.12601i) q^{30} +(4.16277 + 7.21013i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.05235 + 11.3915i) q^{33} +(-2.76777 + 4.79391i) q^{34} +(-4.01441 - 6.03021i) q^{35} +(-0.739071 + 1.28011i) q^{36} +(-2.18595 - 0.585723i) q^{37} +(2.18831 + 0.586356i) q^{38} +12.8745 q^{39} +(2.00378 + 0.992405i) q^{40} +0.597885 q^{41} +(-4.84776 + 4.84776i) q^{42} +(-1.07869 + 6.46811i) q^{43} -5.57301i q^{44} +(-3.24061 - 0.650342i) q^{45} +(5.04122 - 2.91055i) q^{46} +(-0.810206 - 0.810206i) q^{47} +(0.547703 - 2.04406i) q^{48} +(-3.02744 + 1.74789i) q^{49} +(-0.669527 + 4.95497i) q^{50} +11.7141i q^{51} +(-5.87660 + 1.57463i) q^{52} +(3.65040 + 0.978121i) q^{53} -3.22050i q^{54} +(11.8071 - 3.98554i) q^{55} +(1.61986 - 2.80568i) q^{56} +(4.63082 - 1.24082i) q^{57} +(-1.00438 - 3.74840i) q^{58} +2.68055i q^{59} +(4.72227 - 0.301431i) q^{60} +(0.146321 + 0.0844784i) q^{61} +(-8.04185 - 2.15481i) q^{62} +(-1.23942 + 4.62559i) q^{63} +1.00000i q^{64} +(-7.53870 - 11.3242i) q^{65} +(-5.89670 - 10.2134i) q^{66} +(-0.883904 + 3.29877i) q^{67} +(-1.43270 - 5.34691i) q^{68} +(6.15919 - 10.6680i) q^{69} +(7.10262 + 1.42539i) q^{70} +(-9.38650 - 5.41930i) q^{71} +(-0.382571 - 1.42778i) q^{72} +(4.08032 - 1.09332i) q^{73} +(1.95987 - 1.13153i) q^{74} +(4.01575 + 9.78914i) q^{75} +(-1.96198 + 1.13275i) q^{76} +(-4.67298 - 17.4398i) q^{77} +(-9.10367 + 9.10367i) q^{78} +(7.80903 + 4.50855i) q^{79} +(-2.11862 + 0.715150i) q^{80} +(-5.62476 - 9.74237i) q^{81} +(-0.422769 + 0.422769i) q^{82} +(-0.250492 - 0.0671191i) q^{83} -6.85577i q^{84} +(10.3035 - 6.85920i) q^{85} +(-3.81090 - 5.33639i) q^{86} +(-5.80679 - 5.80679i) q^{87} +(3.94071 + 3.94071i) q^{88} +(-6.27562 - 10.8697i) q^{89} +(2.75132 - 1.83160i) q^{90} +(-17.0695 + 9.85507i) q^{91} +(-1.50661 + 5.62275i) q^{92} +(-17.0179 + 4.55992i) q^{93} +1.14580 q^{94} +(-3.80299 - 3.34662i) q^{95} +(1.05808 + 1.83265i) q^{96} +(-3.08924 - 3.08924i) q^{97} +(0.904776 - 3.37667i) q^{98} +(-7.13406 - 4.11885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) $ 88 * q + 4 * q^6 + 12 * q^7	$ 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) $ 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.547703	+	2.04406i	−0.316217	+	1.18014i	0.606635	+	0.794980i	$0.292519\pi$
$3$	−0.547703	+	2.04406i	−0.316217	+	1.18014i	−0.922852	+	0.385156i	$0.874148\pi$
$4$		−	1.00000i		−	0.500000i
$5$	2.11862	−	0.715150i	0.947477	−	0.319825i
$5$	2.11862	−	0.715150i	0.947477	−	0.319825i
$6$	−1.05808	−	1.83265i	−0.431960	−	0.748176i
$7$	−0.838501	−	3.12933i	−0.316924	−	1.18278i	−0.922185	−	0.386749i	$-0.873598\pi$
$7$	−0.838501	−	3.12933i	−0.316924	−	1.18278i	0.605261	−	0.796027i	$-0.293069\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.28011	−	0.739071i	−0.426703	−	0.246357i
$10$	−0.992405	+	2.00378i	−0.313826	+	0.633651i
$11$	5.57301			1.68033			0.840163	−	0.542334i	$-0.182459\pi$
$11$	5.57301			1.68033			0.840163	+	0.542334i	$0.182459\pi$
$12$	2.04406	+	0.547703i	0.590068	+	0.158108i
$13$	−1.57463	−	5.87660i	−0.436724	−	1.62988i	−0.736907	−	0.675994i	$-0.763715\pi$
$13$	−1.57463	−	5.87660i	−0.436724	−	1.62988i	0.300183	−	0.953882i	$-0.402952\pi$
$14$	2.80568	+	1.61986i	0.749850	+	0.432926i
$15$	0.301431	+	4.72227i	0.0778292	+	1.21929i
$16$	−1.00000			−0.250000
$17$	5.34691	−	1.43270i	1.29682	−	0.347481i	0.456571	−	0.889687i	$-0.349077\pi$
$17$	5.34691	−	1.43270i	1.29682	−	0.347481i	0.840246	+	0.542206i	$0.182411\pi$
$18$	1.42778	−	0.382571i	0.336530	−	0.0901729i
$19$	−1.13275	−	1.96198i	−0.259871	−	0.450110i	0.706336	−	0.707877i	$-0.250347\pi$
$19$	−1.13275	−	1.96198i	−0.259871	−	0.450110i	−0.966207	+	0.257767i	$0.917013\pi$
$20$	−0.715150	−	2.11862i	−0.159912	−	0.473738i
$21$	6.85577			1.49605
$22$	−3.94071	+	3.94071i	−0.840163	+	0.840163i
$23$	−5.62275	−	1.50661i	−1.17242	−	0.314150i	−0.380507	−	0.924778i	$-0.624250\pi$
$23$	−5.62275	−	1.50661i	−1.17242	−	0.314150i	−0.791918	+	0.610628i	$0.790917\pi$
$24$	−1.83265	+	1.05808i	−0.374088	+	0.215980i
$25$	3.97712	−	3.03027i	0.795424	−	0.606053i
$26$	5.26882	+	3.04195i	1.03330	+	0.596576i
$27$	−2.27724	+	2.27724i	−0.438254	+	0.438254i
$28$	−3.12933	+	0.838501i	−0.591388	+	0.158462i
$29$	−1.94032	+	3.36073i	−0.360308	+	0.624071i	−0.988011	−	0.154381i	$-0.950662\pi$
$29$	−1.94032	+	3.36073i	−0.360308	+	0.624071i	0.627704	+	0.778452i	$0.283995\pi$
$30$	−3.55229	−	3.12601i	−0.648557	−	0.570728i
$31$	4.16277	+	7.21013i	0.747655	+	1.29498i	0.948944	+	0.315445i	$0.102154\pi$
$31$	4.16277	+	7.21013i	0.747655	+	1.29498i	−0.201289	+	0.979532i	$0.564513\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−3.05235	+	11.3915i	−0.531347	+	1.98301i
$34$	−2.76777	+	4.79391i	−0.474668	+	0.822149i
$35$	−4.01441	−	6.03021i	−0.678559	−	1.01929i
$36$	−0.739071	+	1.28011i	−0.123178	+	0.213351i
$37$	−2.18595	−	0.585723i	−0.359368	−	0.0962923i	0.0746177	−	0.997212i	$-0.476226\pi$
$37$	−2.18595	−	0.585723i	−0.359368	−	0.0962923i	−0.433985	+	0.900920i	$0.642893\pi$
$38$	2.18831	+	0.586356i	0.354991	+	0.0951195i
$39$	12.8745			2.06157
$40$	2.00378	+	0.992405i	0.316825	+	0.156913i
$41$	0.597885			0.0933740			0.0466870	−	0.998910i	$-0.485134\pi$
$41$	0.597885			0.0933740			0.0466870	+	0.998910i	$0.485134\pi$
$42$	−4.84776	+	4.84776i	−0.748026	+	0.748026i
$43$	−1.07869	+	6.46811i	−0.164498	+	0.986377i
$43$	−1.07869	+	6.46811i	−0.164498	+	0.986377i
$44$		−	5.57301i		−	0.840163i
$45$	−3.24061	−	0.650342i	−0.483082	−	0.0969473i
$46$	5.04122	−	2.91055i	0.743287	−	0.429137i
$47$	−0.810206	−	0.810206i	−0.118181	−	0.118181i	0.645543	−	0.763724i	$-0.276631\pi$
$47$	−0.810206	−	0.810206i	−0.118181	−	0.118181i	−0.763724	+	0.645543i	$0.776631\pi$
$48$	0.547703	−	2.04406i	0.0790541	−	0.295034i
$49$	−3.02744	+	1.74789i	−0.432491	+	0.249699i
$50$	−0.669527	+	4.95497i	−0.0946854	+	0.700739i
$51$			11.7141i			1.64030i
$52$	−5.87660	+	1.57463i	−0.814938	+	0.218362i
$53$	3.65040	+	0.978121i	0.501421	+	0.134355i	0.500659	−	0.865644i	$-0.333091\pi$
$53$	3.65040	+	0.978121i	0.501421	+	0.134355i	0.000761436		1.00000i	$0.499758\pi$
$54$		−	3.22050i		−	0.438254i
$55$	11.8071	−	3.98554i	1.59207	−	0.537410i
$56$	1.61986	−	2.80568i	0.216463	−	0.374925i
$57$	4.63082	−	1.24082i	0.613367	−	0.164351i
$58$	−1.00438	−	3.74840i	−0.131882	−	0.492189i
$59$			2.68055i			0.348978i	0.984659	+	0.174489i	$0.0558273\pi$
$59$			2.68055i			0.348978i	−0.984659	+	0.174489i	$0.944173\pi$
$60$	4.72227	−	0.301431i	0.609643	−	0.0389146i
$61$	0.146321	+	0.0844784i	0.0187345	+	0.0108164i	0.509338	−	0.860567i	$-0.329890\pi$
$61$	0.146321	+	0.0844784i	0.0187345	+	0.0108164i	−0.490604	+	0.871383i	$0.663224\pi$
$62$	−8.04185	−	2.15481i	−1.02132	−	0.273661i
$63$	−1.23942	+	4.62559i	−0.156153	+	0.582770i
$64$			1.00000i			0.125000i
$65$	−7.53870	−	11.3242i	−0.935060	−	1.40459i
$66$	−5.89670	−	10.2134i	−0.725833	−	1.25718i
$67$	−0.883904	+	3.29877i	−0.107986	+	0.403009i	−0.998667	−	0.0516198i	$-0.983562\pi$
$67$	−0.883904	+	3.29877i	−0.107986	+	0.403009i	0.890681	+	0.454629i	$0.150228\pi$
$68$	−1.43270	−	5.34691i	−0.173741	−	0.648409i
$69$	6.15919	−	10.6680i	0.741480	−	1.28428i
$70$	7.10262	+	1.42539i	0.848925	+	0.170367i
$71$	−9.38650	−	5.41930i	−1.11397	−	0.643153i	−0.174117	−	0.984725i	$-0.555707\pi$
$71$	−9.38650	−	5.41930i	−1.11397	−	0.643153i	−0.939855	+	0.341572i	$0.889041\pi$
$72$	−0.382571	−	1.42778i	−0.0450865	−	0.168265i
$73$	4.08032	−	1.09332i	0.477565	−	0.127963i	−0.0120033	−	0.999928i	$-0.503821\pi$
$73$	4.08032	−	1.09332i	0.477565	−	0.127963i	0.489569	+	0.871965i	$0.337154\pi$
$74$	1.95987	−	1.13153i	0.227830	−	0.131538i
$75$	4.01575	+	9.78914i	0.463699	+	1.13035i
$76$	−1.96198	+	1.13275i	−0.225055	+	0.129936i
$77$	−4.67298	−	17.4398i	−0.532535	−	1.98745i
$78$	−9.10367	+	9.10367i	−1.03079	+	1.03079i
$79$	7.80903	+	4.50855i	0.878585	+	0.507251i	0.870192	−	0.492714i	$-0.163995\pi$
$79$	7.80903	+	4.50855i	0.878585	+	0.507251i	0.00839326	+	0.999965i	$0.497328\pi$
$80$	−2.11862	+	0.715150i	−0.236869	+	0.0799562i
$81$	−5.62476	−	9.74237i	−0.624973	−	1.08249i
$82$	−0.422769	+	0.422769i	−0.0466870	+	0.0466870i
$83$	−0.250492	−	0.0671191i	−0.0274951	−	0.00736728i	0.245045	−	0.969512i	$-0.421197\pi$
$83$	−0.250492	−	0.0671191i	−0.0274951	−	0.00736728i	−0.272540	+	0.962144i	$0.587864\pi$
$84$		−	6.85577i		−	0.748026i
$85$	10.3035	−	6.85920i	1.11757	−	0.743985i
$86$	−3.81090	−	5.33639i	−0.410940	−	0.575438i
$87$	−5.80679	−	5.80679i	−0.622554	−	0.622554i
$88$	3.94071	+	3.94071i	0.420081	+	0.420081i
$89$	−6.27562	−	10.8697i	−0.665214	−	1.15218i	−0.979227	−	0.202766i	$-0.935007\pi$
$89$	−6.27562	−	10.8697i	−0.665214	−	1.15218i	0.314013	−	0.949419i	$-0.398326\pi$
$90$	2.75132	−	1.83160i	0.290015	−	0.193067i
$91$	−17.0695	+	9.85507i	−1.78937	+	1.03309i
$92$	−1.50661	+	5.62275i	−0.157075	+	0.586212i
$93$	−17.0179	+	4.55992i	−1.76467	+	0.472842i
$94$	1.14580			0.118181
$95$	−3.80299	−	3.34662i	−0.390178	−	0.343356i
$96$	1.05808	+	1.83265i	0.107990	+	0.187044i
$97$	−3.08924	−	3.08924i	−0.313665	−	0.313665i	0.532663	−	0.846328i	$-0.321191\pi$
$97$	−3.08924	−	3.08924i	−0.313665	−	0.313665i	−0.846328	+	0.532663i	$0.821191\pi$
$98$	0.904776	−	3.37667i	0.0913962	−	0.341095i
$99$	−7.13406	−	4.11885i	−0.717000	−	0.413960i
$100$	−3.03027	−	3.97712i	−0.303027	−	0.397712i
$101$	2.15822	−	3.73814i	0.214751	−	0.371959i	−0.738445	−	0.674314i	$-0.764439\pi$
$101$	2.15822	−	3.73814i	0.214751	−	0.371959i	0.953195	+	0.302355i	$0.0977727\pi$
$102$	−8.28311	−	8.28311i	−0.820150	−	0.820150i
$103$	2.08918	+	7.79694i	0.205853	+	0.768255i	0.989188	+	0.146655i	$0.0468506\pi$
$103$	2.08918	+	7.79694i	0.205853	+	0.768255i	−0.783334	+	0.621601i	$0.786483\pi$
$104$	3.04195	−	5.26882i	0.298288	−	0.516650i
$105$	14.5248	−	4.90291i	1.41747	−	0.478475i
$106$	−3.27286	+	1.88958i	−0.317888	+	0.183533i
$107$	13.1006	+	13.1006i	1.26649	+	1.26649i	0.947891	+	0.318594i	$0.103211\pi$
$107$	13.1006	+	13.1006i	1.26649	+	1.26649i	0.318594	+	0.947891i	$0.396789\pi$
$108$	2.27724	+	2.27724i	0.219127	+	0.219127i
$109$	−11.2224	+	6.47927i	−1.07491	+	0.620601i	−0.929520	−	0.368772i	$-0.879778\pi$
$109$	−11.2224	+	6.47927i	−1.07491	+	0.620601i	−0.145393	+	0.989374i	$0.546445\pi$
$110$	−5.53068	+	11.1671i	−0.527330	+	1.06474i
$111$	2.39450	−	4.14740i	0.227276	−	0.393653i
$112$	0.838501	+	3.12933i	0.0792309	+	0.295694i
$113$	14.9496	+	14.9496i	1.40634	+	1.40634i	0.777675	+	0.628666i	$0.216399\pi$
$113$	14.9496	+	14.9496i	1.40634	+	1.40634i	0.628666	+	0.777675i	$0.283601\pi$
$114$	−2.39709	+	4.15188i	−0.224508	+	0.388859i
$115$	−12.9899	+	0.829171i	−1.21132	+	0.0773206i
$116$	3.36073	+	1.94032i	0.312036	+	0.180154i
$117$	−2.32753	+	8.68645i	−0.215180	+	0.803062i
$118$	−1.89544	−	1.89544i	−0.174489	−	0.174489i
$119$	−8.96679	−	15.5309i	−0.821984	−	1.42372i
$120$	−3.12601	+	3.55229i	−0.285364	+	0.324279i
$121$	20.0584			1.82350
$122$	−0.163200	+	0.0437292i	−0.0147754	+	0.00395906i
$123$	−0.327464	+	1.22211i	−0.0295264	+	0.110194i
$124$	7.21013	−	4.16277i	0.647488	−	0.373828i
$125$	6.25892	−	9.26423i	0.559815	−	0.828618i
$126$	−2.39438	−	4.14719i	−0.213309	−	0.369461i
$127$	−11.9031	−	11.9031i	−1.05623	−	1.05623i	−0.998322	−	0.0579063i	$-0.981558\pi$
$127$	−11.9031	−	11.9031i	−1.05623	−	1.05623i	−0.0579063	−	0.998322i	$-0.518442\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−12.6304	−	5.74750i	−1.11204	−	0.506039i
$130$	13.3381	+	2.67675i	1.16983	+	0.234767i
$131$			5.17965i			0.452548i	0.974064	+	0.226274i	$0.0726544\pi$
$131$			5.17965i			0.452548i	−0.974064	+	0.226274i	$0.927346\pi$
$132$	11.3915	+	3.05235i	0.991507	+	0.265673i
$133$	−5.18988	+	5.18988i	−0.450020	+	0.450020i
$134$	−1.70757	−	2.95760i	−0.147512	−	0.255498i
$135$	−3.19604	+	6.45317i	−0.275071	+	0.555400i
$136$	4.79391	+	2.76777i	0.411075	+	0.237334i
$137$	−1.67454	+	1.67454i	−0.143066	+	0.143066i	−0.775012	−	0.631946i	$-0.782256\pi$
$137$	−1.67454	+	1.67454i	−0.143066	+	0.143066i	0.631946	+	0.775012i	$0.282256\pi$
$138$	3.18823	+	11.8986i	0.271400	+	1.01288i
$139$	7.24956	−	4.18554i	0.614900	−	0.355013i	−0.159981	−	0.987120i	$-0.551143\pi$
$139$	7.24956	−	4.18554i	0.614900	−	0.355013i	0.774881	+	0.632108i	$0.217810\pi$
$140$	−6.03021	+	4.01441i	−0.509646	+	0.339279i
$141$	2.09986	−	1.21235i	0.176840	−	0.102099i
$142$	10.4693	−	2.80524i	0.878563	−	0.235410i
$143$	−8.77543	−	32.7504i	−0.733838	−	2.73872i
$144$	1.28011	+	0.739071i	0.106676	+	0.0615892i
$145$	−1.70737	+	8.50773i	−0.141790	+	0.706528i
$146$	−2.11213	+	3.65832i	−0.174801	+	0.302764i
$147$	−1.91465	−	7.14558i	−0.157918	−	0.589358i
$148$	−0.585723	+	2.18595i	−0.0481461	+	0.179684i
$149$	−4.69657	−	8.13470i	−0.384758	−	0.666420i	0.606978	−	0.794719i	$-0.292382\pi$
$149$	−4.69657	−	8.13470i	−0.384758	−	0.666420i	−0.991736	+	0.128299i	$0.959048\pi$
$150$	−9.76153	−	4.08240i	−0.797026	−	0.333327i
$151$		−	11.5511i		−	0.940016i	−0.882662	−	0.470008i	$-0.844251\pi$
$151$		−	11.5511i		−	0.940016i	0.882662	−	0.470008i	$-0.155749\pi$
$152$	0.586356	−	2.18831i	0.0475597	−	0.177495i
$153$	−7.90350	−	2.11774i	−0.638960	−	0.171209i
$154$	15.6361	+	9.02750i	1.25999	+	0.727457i
$155$	13.9757	+	12.2985i	1.12255	+	0.987842i
$156$		−	12.8745i		−	1.03079i
$157$	0.785236	+	2.93054i	0.0626687	+	0.233883i	0.990155	−	0.139974i	$-0.0447019\pi$
$157$	0.785236	+	2.93054i	0.0626687	+	0.233883i	−0.927487	+	0.373857i	$0.878035\pi$
$158$	−8.70984	+	2.33380i	−0.692918	+	0.185667i
$159$	−3.99867	+	6.92590i	−0.317115	+	0.549259i
$160$	0.992405	−	2.00378i	0.0784565	−	0.158413i
$161$			18.8587i			1.48628i
$162$	10.8662	+	2.91159i	0.853730	+	0.228756i
$163$	−11.3545	+	3.04243i	−0.889354	+	0.238302i	−0.674439	−	0.738331i	$-0.735614\pi$
$163$	−11.3545	+	3.04243i	−0.889354	+	0.238302i	−0.214915	+	0.976633i	$0.568948\pi$
$164$		−	0.597885i		−	0.0466870i
$165$	1.67988	+	26.3173i	0.130778	+	2.04880i
$166$	0.224585	−	0.129664i	0.0174312	−	0.0100639i
$167$	−4.78796	+	17.8689i	−0.370503	+	1.38274i	0.489302	+	0.872114i	$0.337252\pi$
$167$	−4.78796	+	17.8689i	−0.370503	+	1.38274i	−0.859805	+	0.510622i	$0.829415\pi$
$168$	4.84776	+	4.84776i	0.374013	+	0.374013i
$169$	−20.7966	+	12.0069i	−1.59974	+	0.923611i
$170$	−2.43548	+	12.1359i	−0.186793	+	0.930778i
$171$			3.34874i			0.256084i
$172$	6.46811	+	1.07869i	0.493189	+	0.0822491i
$173$	16.5161	−	16.5161i	1.25569	−	1.25569i	0.302566	−	0.953129i	$-0.402157\pi$
$173$	16.5161	−	16.5161i	1.25569	−	1.25569i	0.953129	−	0.302566i	$-0.0978431\pi$
$174$	8.21205			0.622554
$175$	−12.8175	−	9.90484i	−0.968914	−	0.748735i
$176$	−5.57301			−0.420081
$177$	−5.47919	−	1.46815i	−0.411841	−	0.110353i
$178$	12.1236	+	3.24850i	0.908699	+	0.243485i
$179$	−1.72769	+	2.99245i	−0.129134	+	0.223666i	−0.923341	−	0.383980i	$-0.874553\pi$
$179$	−1.72769	+	2.99245i	−0.129134	+	0.223666i	0.794207	+	0.607647i	$0.207886\pi$
$180$	−0.650342	+	3.24061i	−0.0484736	+	0.241541i
$181$	−11.4633	+	19.8551i	−0.852063	+	1.47582i	0.0272809	+	0.999628i	$0.491315\pi$
$181$	−11.4633	+	19.8551i	−0.852063	+	1.47582i	−0.879344	+	0.476188i	$0.842018\pi$
$182$	5.10136	−	19.0385i	0.378138	−	1.41123i
$183$	−0.252819	+	0.252819i	−0.0186889	+	0.0186889i
$184$	−2.91055	−	5.04122i	−0.214569	−	0.371644i
$185$	−5.05008	+	0.322356i	−0.371289	+	0.0237000i
$186$	8.80909	−	15.2578i	0.645914	−	1.11876i
$187$	29.7984	−	7.98446i	2.17908	−	0.583882i
$188$	−0.810206	+	0.810206i	−0.0590904	+	0.0590904i
$189$	9.03569	+	5.21676i	0.657250	+	0.379463i
$190$	5.05553	−	0.322704i	0.366767	−	0.0234114i
$191$	−2.33866	+	1.35023i	−0.169220	+	0.0976991i	−0.582218	−	0.813033i	$-0.697815\pi$
$191$	−2.33866	+	1.35023i	−0.169220	+	0.0976991i	0.412998	+	0.910732i	$0.364482\pi$
$192$	−2.04406	−	0.547703i	−0.147517	−	0.0395271i
$193$	−5.87517	+	5.87517i	−0.422904	+	0.422904i	−0.886202	−	0.463298i	$-0.846666\pi$
$193$	−5.87517	+	5.87517i	−0.422904	+	0.422904i	0.463298	+	0.886202i	$0.346666\pi$
$194$	4.36885			0.313665
$195$	27.2763	−	9.20722i	1.95329	−	0.659343i
$196$	1.74789	+	3.02744i	0.124850	+	0.216246i
$197$	−11.8091	+	3.16424i	−0.841365	+	0.225443i	−0.653666	−	0.756784i	$-0.726770\pi$
$197$	−11.8091	+	3.16424i	−0.841365	+	0.225443i	−0.187699	+	0.982227i	$0.560103\pi$
$198$	7.95701	−	2.13207i	0.565480	−	0.151520i
$199$	−22.4903			−1.59430			−0.797149	−	0.603782i	$-0.793660\pi$
$199$	−22.4903			−1.59430			−0.797149	+	0.603782i	$0.793660\pi$
$200$	4.95497	+	0.669527i	0.350369	+	0.0473427i
$201$	−6.25876	−	3.61350i	−0.441459	−	0.254877i
$202$	1.11718	+	4.16936i	0.0786042	+	0.293355i
$203$	12.1438	+	3.25392i	0.852326	+	0.228380i
$204$	11.7141			0.820150
$205$	1.26669	−	0.427578i	0.0884697	−	0.0298633i
$206$	−6.99055	−	4.03599i	−0.487054	−	0.281201i
$207$	6.08424	+	6.08424i	0.422884	+	0.422884i
$208$	1.57463	+	5.87660i	0.109181	+	0.407469i
$209$	−6.31284	−	10.9342i	−0.436668	−	0.756332i
$210$	−6.80370	+	13.7375i	−0.469500	+	0.947975i
$211$			6.00793i			0.413603i	0.978383	+	0.206801i	$0.0663054\pi$
$211$			6.00793i			0.413603i	−0.978383	+	0.206801i	$0.933695\pi$
$212$	0.978121	−	3.65040i	0.0671776	−	0.250710i
$213$	16.2184	−	16.2184i	1.11126	−	1.11126i
$214$	−18.5271			−1.26649
$215$	2.34034	+	14.4749i	0.159610	+	0.987180i
$216$	−3.22050			−0.219127
$217$	19.0724	−	19.0724i	1.29472	−	1.29472i
$218$	3.35392	−	12.5170i	0.227156	−	0.847757i
$219$			8.93922i			0.604056i
$220$	−3.98554	−	11.8071i	−0.268705	−	0.796035i
$221$	−16.8388	−	29.1657i	−1.13270	−	1.96190i
$222$	1.23948	+	4.62582i	0.0831888	+	0.310465i
$223$	2.43880	+	2.43880i	0.163314	+	0.163314i	0.784033	−	0.620719i	$-0.213159\pi$
$223$	2.43880	+	2.43880i	0.163314	+	0.163314i	−0.620719	+	0.784033i	$0.713159\pi$
$224$	−2.80568	−	1.61986i	−0.187462	−	0.108231i
$225$	−7.33073	+	0.939696i	−0.488715	+	0.0626464i
$226$	−21.1419			−1.40634
$227$	0.182120	+	0.0487988i	0.0120877	+	0.00323889i	0.264858	−	0.964287i	$-0.414675\pi$
$227$	0.182120	+	0.0487988i	0.0120877	+	0.00323889i	−0.252770	+	0.967526i	$0.581342\pi$
$228$	−1.24082	−	4.63082i	−0.0821756	−	0.306683i
$229$	24.6528	+	14.2333i	1.62910	+	0.940562i	0.984361	+	0.176160i	$0.0563678\pi$
$229$	24.6528	+	14.2333i	1.62910	+	0.940562i	0.644740	+	0.764402i	$0.276966\pi$
$230$	8.59896	−	9.77158i	0.566998	−	0.644319i
$231$	38.2073			2.51386
$232$	−3.74840	+	1.00438i	−0.246095	+	0.0659409i
$233$	−1.68596	+	0.451751i	−0.110451	+	0.0295952i	−0.313621	−	0.949548i	$-0.601542\pi$
$233$	−1.68596	+	0.451751i	−0.110451	+	0.0295952i	0.203170	+	0.979143i	$0.434876\pi$
$234$	−4.49644	−	7.78806i	−0.293941	−	0.509121i
$235$	−2.29594	−	1.13710i	−0.149771	−	0.0741763i
$236$	2.68055			0.174489
$237$	−13.4928	+	13.4928i	−0.876448	+	0.876448i
$238$	17.3225	+	4.64155i	1.12285	+	0.300867i
$239$	24.2239	−	13.9857i	1.56691	−	0.904657i	0.570386	−	0.821377i	$-0.306794\pi$
$239$	24.2239	−	13.9857i	1.56691	−	0.904657i	0.996526	−	0.0832798i	$-0.0265395\pi$
$240$	−0.301431	−	4.72227i	−0.0194573	−	0.304821i
$241$	13.5239	+	7.80800i	0.871148	+	0.502958i	0.867730	−	0.497036i	$-0.165578\pi$
$241$	13.5239	+	7.80800i	0.871148	+	0.502958i	0.00341865	+	0.999994i	$0.498912\pi$
$242$	−14.1835	+	14.1835i	−0.911748	+	0.911748i
$243$	13.6624	−	3.66082i	0.876441	−	0.234842i
$244$	0.0844784	−	0.146321i	0.00540818	−	0.00936723i
$245$	−5.16400	+	5.86820i	−0.329916	+	0.374906i
$246$	−0.632611	−	1.09571i	−0.0403338	−	0.0698602i
$247$	−9.74613	+	9.74613i	−0.620131	+	0.620131i
$248$	−2.15481	+	8.04185i	−0.136830	+	0.510658i
$249$	0.274390	−	0.475258i	0.0173888	−	0.0301183i
$250$	2.12507	+	10.9765i	0.134402	+	0.694216i
$251$	−5.66275	+	9.80818i	−0.357430	+	0.619087i	−0.987531	−	0.157427i	$-0.949680\pi$
$251$	−5.66275	+	9.80818i	−0.357430	+	0.619087i	0.630101	+	0.776513i	$0.283014\pi$
$252$	4.62559	+	1.23942i	0.291385	+	0.0780764i
$253$	−31.3356	−	8.39636i	−1.97005	−	0.527875i
$254$	16.8335			1.05623
$255$	8.37733	+	24.8177i	0.524609	+	1.55415i
$256$	1.00000			0.0625000
$257$	−18.9632	+	18.9632i	−1.18289	+	1.18289i	−0.203897	+	0.978992i	$0.565361\pi$
$257$	−18.9632	+	18.9632i	−1.18289	+	1.18289i	−0.978992	+	0.203897i	$0.934639\pi$
$258$	12.9951	−	4.86693i	0.809041	−	0.303002i
$259$			7.33168i			0.455568i
$260$	−11.3242	+	7.53870i	−0.702297	+	0.467530i
$261$	4.96763	−	2.86806i	0.307489	−	0.177529i
$262$	−3.66256	−	3.66256i	−0.226274	−	0.226274i
$263$	−2.81727	+	10.5142i	−0.173720	+	0.648333i	0.823046	+	0.567975i	$0.192273\pi$
$263$	−2.81727	+	10.5142i	−0.173720	+	0.648333i	−0.996766	+	0.0803582i	$0.974394\pi$
$264$	−10.2134	+	5.89670i	−0.628590	+	0.362917i
$265$	8.43332	−	0.538314i	0.518055	−	0.0330684i
$266$		−	7.33960i		−	0.450020i
$267$	25.6554	−	6.87435i	1.57009	−	0.420703i
$268$	3.29877	+	0.883904i	0.201505	+	0.0539930i
$269$			2.14172i			0.130583i	0.997866	+	0.0652915i	$0.0207977\pi$
$269$			2.14172i			0.130583i	−0.997866	+	0.0652915i	$0.979202\pi$
$270$	−2.30314	−	6.82302i	−0.140165	−	0.415236i
$271$	0.682303	−	1.18178i	0.0414470	−	0.0717883i	−0.844558	−	0.535464i	$-0.820137\pi$
$271$	0.682303	−	1.18178i	0.0414470	−	0.0717883i	0.886005	+	0.463676i	$0.153470\pi$
$272$	−5.34691	+	1.43270i	−0.324204	+	0.0868703i
$273$	−10.7953	−	40.2886i	−0.653362	−	2.43838i
$274$		−	2.36816i		−	0.143066i
$275$	22.1645	−	16.8877i	1.33657	−	1.01837i
$276$	−10.6680	−	6.15919i	−0.642140	−	0.370740i
$277$	6.18355	+	1.65688i	0.371534	+	0.0995521i	0.439754	−	0.898118i	$-0.355066\pi$
$277$	6.18355	+	1.65688i	0.371534	+	0.0995521i	−0.0682207	+	0.997670i	$0.521732\pi$
$278$	−2.16659	+	8.08584i	−0.129944	+	0.484956i
$279$		−	12.3063i		−	0.736760i
$280$	1.42539	−	7.10262i	0.0851833	−	0.424463i
$281$	−6.48912	−	11.2395i	−0.387109	−	0.670492i	0.604951	−	0.796263i	$-0.293193\pi$
$281$	−6.48912	−	11.2395i	−0.387109	−	0.670492i	−0.992059	+	0.125771i	$0.959859\pi$
$282$	−0.627561	+	2.34209i	−0.0373707	+	0.139469i
$283$	6.09650	+	22.7525i	0.362399	+	1.35249i	0.870912	+	0.491439i	$0.163529\pi$
$283$	6.09650	+	22.7525i	0.362399	+	1.35249i	−0.508513	+	0.861054i	$0.669805\pi$
$284$	−5.41930	+	9.38650i	−0.321576	+	0.556986i
$285$	8.92358	−	5.94057i	0.528587	−	0.351889i
$286$	29.3632	+	16.9528i	1.73628	+	1.00244i
$287$	−0.501327	−	1.87098i	−0.0295924	−	0.110440i
$288$	−1.42778	+	0.382571i	−0.0841325	+	0.0225432i
$289$	11.8144	−	6.82107i	0.694967	−	0.401239i
$290$	−4.80858	−	7.22317i	−0.282369	−	0.424159i
$291$	8.00656	−	4.62259i	0.469353	−	0.270981i
$292$	−1.09332	−	4.08032i	−0.0639816	−	0.238783i
$293$	−9.16945	+	9.16945i	−0.535685	+	0.535685i	−0.922259	−	0.386573i	$-0.873659\pi$
$293$	−9.16945	+	9.16945i	−0.535685	+	0.535685i	0.386573	+	0.922259i	$0.373659\pi$
$294$	6.40655	+	3.69883i	0.373638	+	0.215720i
$295$	1.91700	+	5.67907i	0.111612	+	0.330648i
$296$	−1.13153	−	1.95987i	−0.0657688	−	0.113915i
$297$	−12.6911	+	12.6911i	−0.736410	+	0.736410i
$298$	9.07307	+	2.43112i	0.525589	+	0.140831i
$299$			35.4150i			2.04810i
$300$	9.78914	−	4.01575i	0.565176	−	0.231850i
$301$	21.1453	−	2.04795i	1.21880	−	0.118042i
$302$	8.16787	+	8.16787i	0.470008	+	0.470008i
$303$	6.45891	+	6.45891i	0.371055	+	0.371055i
$304$	1.13275	+	1.96198i	0.0649678	+	0.112528i
$305$	0.370413	+	0.0743364i	0.0212098	+	0.00425649i
$306$	7.08608	−	4.09115i	0.405084	−	0.233876i
$307$	6.41507	−	23.9414i	0.366127	−	1.36641i	−0.499759	−	0.866164i	$-0.666578\pi$
$307$	6.41507	−	23.9414i	0.366127	−	1.36641i	0.865886	−	0.500241i	$-0.166755\pi$
$308$	−17.4398	+	4.67298i	−0.993724	+	0.266268i
$309$	−17.0816			−0.971740
$310$	−18.5787	+	1.18591i	−1.05520	+	0.0673551i
$311$	−6.14757	−	10.6479i	−0.348597	−	0.603787i	0.637404	−	0.770530i	$-0.280008\pi$
$311$	−6.14757	−	10.6479i	−0.348597	−	0.603787i	−0.986000	+	0.166743i	$0.946675\pi$
$312$	9.10367	+	9.10367i	0.515394	+	0.515394i
$313$	−5.39516	+	20.1350i	−0.304952	+	1.13810i	0.628034	+	0.778186i	$0.283860\pi$
$313$	−5.39516	+	20.1350i	−0.304952	+	1.13810i	−0.932986	+	0.359911i	$0.882807\pi$
$314$	−2.62745	−	1.51696i	−0.148276	−	0.0856070i
$315$	0.682123	+	10.6863i	0.0384333	+	0.602102i
$316$	4.50855	−	7.80903i	0.253626	−	0.439292i
$317$	−11.5754	−	11.5754i	−0.650140	−	0.650140i	0.302887	−	0.953027i	$-0.402050\pi$
$317$	−11.5754	−	11.5754i	−0.650140	−	0.650140i	−0.953027	+	0.302887i	$0.902050\pi$
$318$	−2.06986	−	7.72483i	−0.116072	−	0.433187i
$319$	−10.8134	+	18.7294i	−0.605434	+	1.04864i
$320$	0.715150	+	2.11862i	0.0399781	+	0.118435i
$321$	−33.9537	+	19.6032i	−1.89511	+	1.09414i
$322$	−13.3351	−	13.3351i	−0.743138	−	0.743138i
$323$	−8.86767	−	8.86767i	−0.493410	−	0.493410i
$324$	−9.74237	+	5.62476i	−0.541243	+	0.312487i
$325$	−24.0702	−	18.6004i	−1.33517	−	1.03176i
$326$	5.87753	−	10.1802i	0.325526	−	0.563828i
$327$	−7.09743	−	26.4880i	−0.392489	−	1.46479i
$328$	0.422769	+	0.422769i	0.0233435	+	0.0233435i
$329$	−1.85604	+	3.21476i	−0.102327	+	0.177236i
$330$	−19.7970	−	17.4213i	−1.08979	−	0.959009i
$331$	−13.1385	−	7.58550i	−0.722156	−	0.416937i	0.0933898	−	0.995630i	$-0.470230\pi$
$331$	−13.1385	−	7.58550i	−0.722156	−	0.416937i	−0.815546	+	0.578693i	$0.803563\pi$
$332$	−0.0671191	+	0.250492i	−0.00368364	+	0.0137475i
$333$	2.36536	+	2.36536i	0.129621	+	0.129621i
$334$	−9.24962	−	16.0208i	−0.506117	−	0.876620i
$335$	0.486461	+	7.62098i	0.0265782	+	0.416379i
$336$	−6.85577			−0.374013
$337$	−22.8640	+	6.12639i	−1.24548	+	0.333726i	−0.820589	−	0.571518i	$-0.806355\pi$
$337$	−22.8640	+	6.12639i	−1.24548	+	0.333726i	−0.424892	+	0.905244i	$0.639688\pi$
$338$	6.21525	−	23.1956i	0.338065	−	1.26168i
$339$	−38.7458	+	22.3699i	−2.10438	+	1.21497i
$340$	−6.85920	−	10.3035i	−0.371992	−	0.558786i
$341$	23.1992	+	40.1821i	1.25630	+	2.17598i
$342$	−2.36791	−	2.36791i	−0.128042	−	0.128042i
$343$	−8.02755	−	8.02755i	−0.433447	−	0.433447i
$344$	−5.33639	+	3.81090i	−0.287719	+	0.205470i
$345$	5.41975	−	27.0063i	0.291790	−	1.45397i
$346$			23.3573i			1.25569i
$347$	−32.5346	−	8.71761i	−1.74655	−	0.467986i	−0.762664	−	0.646795i	$-0.776109\pi$
$347$	−32.5346	−	8.71761i	−1.74655	−	0.467986i	−0.983884	+	0.178809i	$0.942776\pi$
$348$	−5.80679	+	5.80679i	−0.311277	+	0.311277i
$349$	4.98953	+	8.64211i	0.267083	+	0.462602i	0.968107	−	0.250536i	$-0.0806068\pi$
$349$	4.98953	+	8.64211i	0.267083	+	0.462602i	−0.701024	+	0.713138i	$0.747273\pi$
$350$	16.0671	−	2.05958i	0.858824	−	0.110089i
$351$	16.9682	+	9.79660i	0.905696	+	0.522904i
$352$	3.94071	−	3.94071i	0.210041	−	0.210041i
$353$	−6.16727	−	23.0166i	−0.328251	−	1.22505i	−0.911003	−	0.412399i	$-0.864691\pi$
$353$	−6.16727	−	23.0166i	−0.328251	−	1.22505i	0.582752	−	0.812650i	$-0.301976\pi$
$354$	4.91251	−	2.83624i	0.261097	−	0.150744i
$355$	−23.7621	−	4.76869i	−1.26116	−	0.253096i
$356$	−10.8697	+	6.27562i	−0.576092	+	0.332607i
$357$	36.6572	−	9.82228i	1.94011	−	0.519850i
$358$	−0.894320	−	3.33765i	−0.0472663	−	0.176400i
$359$	1.69082	+	0.976196i	0.0892381	+	0.0515217i	0.543955	−	0.839114i	$-0.316926\pi$
$359$	1.69082	+	0.976196i	0.0892381	+	0.0515217i	−0.454717	+	0.890636i	$0.650260\pi$
$360$	−1.83160	−	2.75132i	−0.0965337	−	0.145007i
$361$	6.93374	−	12.0096i	0.364934	−	0.632084i
$362$	−5.93386	−	22.1455i	−0.311877	−	1.16394i
$363$	−10.9861	+	41.0006i	−0.576619	+	2.15197i
$364$	9.85507	+	17.0695i	0.516546	+	0.894684i
$365$	7.86277	−	5.23437i	0.411556	−	0.273980i
$366$		−	0.357540i		−	0.0186889i
$367$	3.04468	−	11.3629i	0.158931	−	0.593139i	−0.839806	−	0.542887i	$-0.817331\pi$
$367$	3.04468	−	11.3629i	0.158931	−	0.593139i	0.998737	−	0.0502515i	$-0.0160023\pi$
$368$	5.62275	+	1.50661i	0.293106	+	0.0785375i
$369$	−0.765358	−	0.441880i	−0.0398429	−	0.0230033i
$370$	3.34300	−	3.79888i	0.173795	−	0.197495i
$371$		−	12.2435i		−	0.635648i
$372$	4.55992	+	17.0179i	0.236421	+	0.882335i
$373$	19.2115	−	5.14770i	0.994732	−	0.266538i	0.275495	−	0.961302i	$-0.411158\pi$
$373$	19.2115	−	5.14770i	0.994732	−	0.266538i	0.719237	+	0.694765i	$0.244492\pi$
$374$	−15.4248	+	26.7165i	−0.797597	+	1.38148i
$375$	15.5086	+	17.8676i	0.800859	+	0.922680i
$376$		−	1.14580i		−	0.0590904i
$377$	22.8049	+	6.11056i	1.17451	+	0.314710i
$378$	−10.0780	+	2.70039i	−0.518356	+	0.138893i
$379$		−	23.5609i		−	1.21024i	−0.796134	−	0.605121i	$-0.793125\pi$
$379$		−	23.5609i		−	1.21024i	0.796134	−	0.605121i	$-0.206875\pi$
$380$	−3.34662	+	3.80299i	−0.171678	+	0.195089i
$381$	30.8499	−	17.8112i	1.58049	−	0.912496i
$382$	0.698930	−	2.60844i	0.0357604	−	0.133459i
$383$	−10.0505	−	10.0505i	−0.513558	−	0.513558i	0.402057	−	0.915615i	$-0.368295\pi$
$383$	−10.0505	−	10.0505i	−0.513558	−	0.513558i	−0.915615	+	0.402057i	$0.868295\pi$
$384$	1.83265	−	1.05808i	0.0935220	−	0.0539950i
$385$	−22.3723	−	33.6064i	−1.14020	−	1.71274i
$386$		−	8.30874i		−	0.422904i
$387$	6.16123	−	7.48265i	0.313193	−	0.380365i
$388$	−3.08924	+	3.08924i	−0.156832	+	0.156832i
$389$	18.4087			0.933360			0.466680	−	0.884426i	$-0.345450\pi$
$389$	18.4087			0.933360			0.466680	+	0.884426i	$0.345450\pi$
$390$	−12.7767	+	25.7977i	−0.646975	+	1.30632i
$391$	−32.2229			−1.62958
$392$	−3.37667	−	0.904776i	−0.170548	−	0.0456981i
$393$	−10.5875	−	2.83691i	−0.534068	−	0.143103i
$394$	6.11285	−	10.5878i	0.307961	−	0.533404i
$395$	19.7687	+	3.96728i	0.994670	+	0.199615i
$396$	−4.11885	+	7.13406i	−0.206980	+	0.358500i
$397$	−1.92730	+	7.19278i	−0.0967283	+	0.360995i	−0.997276	−	0.0737626i	$-0.976499\pi$
$397$	−1.92730	+	7.19278i	−0.0967283	+	0.360995i	0.900547	+	0.434758i	$0.143166\pi$
$398$	15.9031	−	15.9031i	0.797149	−	0.797149i
$399$	−7.76589	−	13.4509i	−0.388781	−	0.673388i
$400$	−3.97712	+	3.03027i	−0.198856	+	0.151513i
$401$	−0.840062	+	1.45503i	−0.0419507	+	0.0726607i	−0.886238	−	0.463229i	$-0.846691\pi$
$401$	−0.840062	+	1.45503i	−0.0419507	+	0.0726607i	0.844288	+	0.535890i	$0.180024\pi$
$402$	6.98074	−	1.87048i	0.348168	−	0.0932913i
$403$	35.8162	−	35.8162i	1.78413	−	1.78413i
$404$	−3.73814	−	2.15822i	−0.185980	−	0.107375i
$405$	−18.8840	−	16.6179i	−0.938354	−	0.825748i
$406$	−10.8878	+	6.28608i	−0.540353	+	0.311973i
$407$	−12.1823	−	3.26424i	−0.603855	−	0.161802i
$408$	−8.28311	+	8.28311i	−0.410075	+	0.410075i
$409$	5.61413			0.277601			0.138800	−	0.990320i	$-0.455675\pi$
$409$	5.61413			0.277601			0.138800	+	0.990320i	$0.455675\pi$
$410$	−0.593344	+	1.19803i	−0.0293032	+	0.0591665i
$411$	−2.50571	−	4.34001i	−0.123597	−	0.214077i
$412$	7.79694	−	2.08918i	0.384128	−	0.102927i
$413$	8.38833	−	2.24765i	0.412763	−	0.110599i
$414$	−8.60441			−0.422884
$415$	−0.578698	+	0.0369393i	−0.0284072	+	0.00181328i
$416$	−5.26882	−	3.04195i	−0.258325	−	0.149144i
$417$	4.58486	+	17.1109i	0.224522	+	0.837926i
$418$	12.1955	+	3.26777i	0.596500	+	0.159832i
$419$	22.8519			1.11639			0.558193	−	0.829711i	$-0.311495\pi$
$419$	22.8519			1.11639			0.558193	+	0.829711i	$0.311495\pi$
$420$	−4.90291	−	14.5248i	−0.239237	−	0.708737i
$421$	−22.9694	−	13.2614i	−1.11946	−	0.646322i	−0.178199	−	0.983995i	$-0.557027\pi$
$421$	−22.9694	−	13.2614i	−1.11946	−	0.646322i	−0.941264	+	0.337673i	$0.890360\pi$
$422$	−4.24825	−	4.24825i	−0.206801	−	0.206801i
$423$	0.438352	+	1.63595i	0.0213134	+	0.0795427i
$424$	1.88958	+	3.27286i	0.0917664	+	0.158944i
$425$	16.9239	−	21.9006i	0.820928	−	1.06234i
$426$			22.9362i			1.11126i
$427$	0.141671	−	0.528722i	0.00685592	−	0.0255866i
$428$	13.1006	−	13.1006i	0.633243	−	0.633243i
$429$	71.7499			3.46412
$430$	−11.8902	−	8.58043i	−0.573395	−	0.413785i
$431$	−14.9598			−0.720586			−0.360293	−	0.932839i	$-0.617323\pi$
$431$	−14.9598			−0.720586			−0.360293	+	0.932839i	$0.617323\pi$
$432$	2.27724	−	2.27724i	0.109564	−	0.109564i
$433$	−3.27515	+	12.2230i	−0.157394	+	0.587401i	0.841495	+	0.540265i	$0.181676\pi$
$433$	−3.27515	+	12.2230i	−0.157394	+	0.587401i	−0.998888	+	0.0471360i	$0.984991\pi$
$434$			26.9724i			1.29472i
$435$	−16.4551	−	8.14967i	−0.788963	−	0.390747i
$436$	6.47927	+	11.2224i	0.310301	+	0.537457i
$437$	3.41323	+	12.7384i	0.163277	+	0.609358i
$438$	−6.32098	−	6.32098i	−0.302028	−	0.302028i
$439$	−24.2592	−	14.0061i	−1.15783	−	0.668472i	−0.207046	−	0.978331i	$-0.566385\pi$
$439$	−24.2592	−	14.0061i	−1.15783	−	0.668472i	−0.950783	+	0.309859i	$0.899718\pi$
$440$	11.1671	+	5.53068i	0.532370	+	0.263665i
$441$	5.16727			0.246060
$442$	32.5301	+	8.71642i	1.54730	+	0.414598i
$443$	−8.40329	−	31.3615i	−0.399252	−	1.49003i	−0.814415	−	0.580283i	$-0.802942\pi$
$443$	−8.40329	−	31.3615i	−0.399252	−	1.49003i	0.415163	−	0.909747i	$-0.363725\pi$
$444$	−4.14740	−	2.39450i	−0.196827	−	0.113638i
$445$	−21.0691	−	18.5407i	−0.998772	−	0.878916i
$446$	−3.44899			−0.163314
$447$	19.2001	−	5.14465i	0.908133	−	0.243334i
$448$	3.12933	−	0.838501i	0.147847	−	0.0396155i
$449$	−0.670606	−	1.16152i	−0.0316479	−	0.0548157i	0.849768	−	0.527157i	$-0.176742\pi$
$449$	−0.670606	−	1.16152i	−0.0316479	−	0.0548157i	−0.881416	+	0.472342i	$0.843409\pi$
$450$	4.51914	−	5.84807i	0.213034	−	0.275681i
$451$	3.33202			0.156899
$452$	14.9496	−	14.9496i	0.703171	−	0.703171i
$453$	23.6111	+	6.32658i	1.10935	+	0.297249i
$454$	−0.163284	+	0.0942721i	−0.00766330	+	0.00442441i
$455$	−29.1159	+	33.0864i	−1.36498	+	1.55112i
$456$	4.15188	+	2.39709i	0.194429	+	0.112254i
$457$	−15.5370	+	15.5370i	−0.726791	+	0.726791i	−0.969979	−	0.243188i	$-0.921807\pi$
$457$	−15.5370	+	15.5370i	−0.726791	+	0.726791i	0.243188	+	0.969979i	$0.421807\pi$
$458$	−27.4966	+	7.36769i	−1.28483	+	0.344270i
$459$	−8.91359	+	15.4388i	−0.416051	+	0.720621i
$460$	0.829171	+	12.9899i	0.0386603	+	0.605659i
$461$	−1.81436	−	3.14257i	−0.0845033	−	0.146364i	0.820676	−	0.571394i	$-0.193597\pi$
$461$	−1.81436	−	3.14257i	−0.0845033	−	0.146364i	−0.905179	+	0.425030i	$0.860264\pi$
$462$	−27.0166	+	27.0166i	−1.25693	+	1.25693i
$463$	3.41511	−	12.7454i	0.158713	−	0.592327i	−0.840045	−	0.542516i	$-0.817472\pi$
$463$	3.41511	−	12.7454i	0.158713	−	0.592327i	0.998759	−	0.0498104i	$-0.0158617\pi$
$464$	1.94032	−	3.36073i	0.0900769	−	0.156018i
$465$	−32.7934	+	21.8311i	−1.52076	+	1.01239i
$466$	0.872717	−	1.51159i	0.0404278	−	0.0700230i
$467$	21.3729	+	5.72685i	0.989019	+	0.265007i	0.716839	−	0.697239i	$-0.245588\pi$
$467$	21.3729	+	5.72685i	0.989019	+	0.265007i	0.272181	+	0.962246i	$0.412255\pi$
$468$	8.68645	+	2.32753i	0.401531	+	0.107590i
$469$	11.0641			0.510893
$470$	2.42753	−	0.819423i	0.111973	−	0.0377971i
$471$	−6.42027			−0.295830
$472$	−1.89544	+	1.89544i	−0.0872445	+	0.0872445i
$473$	−6.01153	+	36.0468i	−0.276411	+	1.65744i
$474$		−	19.0816i		−	0.876448i
$475$	−10.4504	−	4.37051i	−0.479498	−	0.200533i
$476$	−15.5309	+	8.96679i	−0.711859	+	0.410992i
$477$	−3.95000	−	3.95000i	−0.180858	−	0.180858i
$478$	−7.23951	+	27.0182i	−0.331127	+	1.23578i
$479$	15.4948	−	8.94593i	0.707976	−	0.408750i	−0.102335	−	0.994750i	$-0.532631\pi$
$479$	15.4948	−	8.94593i	0.707976	−	0.408750i	0.810311	+	0.586000i	$0.199298\pi$
$480$	3.55229	+	3.12601i	0.162139	+	0.142682i
$481$			13.7682i			0.627778i
$482$	−15.0839	+	4.04172i	−0.687053	+	0.184095i
$483$	−38.5483	−	10.3290i	−1.75401	−	0.469985i
$484$		−	20.0584i		−	0.911748i
$485$	−8.75420	−	4.33566i	−0.397508	−	0.196872i
$486$	−7.07216	+	12.2493i	−0.320800	+	0.555641i
$487$	20.2213	−	5.41828i	0.916314	−	0.245525i	0.230305	−	0.973119i	$-0.426028\pi$
$487$	20.2213	−	5.41828i	0.916314	−	0.245525i	0.686009	+	0.727593i	$0.259361\pi$
$488$	0.0437292	+	0.163200i	0.00197953	+	0.00738771i
$489$		−	24.8756i		−	1.12491i
$490$	−0.497948	−	7.80094i	−0.0224950	−	0.352411i
$491$	7.86834	+	4.54279i	0.355093	+	0.205013i	0.666926	−	0.745124i	$-0.267610\pi$
$491$	7.86834	+	4.54279i	0.355093	+	0.205013i	−0.311833	+	0.950137i	$0.600943\pi$
$492$	1.22211	+	0.327464i	0.0550970	+	0.0147632i
$493$	−5.55979	+	20.7494i	−0.250400	+	0.934507i
$494$		−	13.7831i		−	0.620131i
$495$	−18.0600	−	3.62436i	−0.811735	−	0.162903i
$496$	−4.16277	−	7.21013i	−0.186914	−	0.323744i
$497$	−9.08818	+	33.9175i	−0.407661	+	1.52141i
$498$	0.142035	+	0.530082i	0.00636474	+	0.0237535i
$499$	−10.4449	+	18.0911i	−0.467579	+	0.809870i	−0.999314	−	0.0370404i	$-0.988207\pi$
$499$	−10.4449	+	18.0911i	−0.467579	+	0.809870i	0.531735	+	0.846911i	$0.321540\pi$
$500$	−9.26423	−	6.25892i	−0.414309	−	0.279907i
$501$	−33.9026	−	19.5737i	−1.51466	−	0.874488i
$502$	−2.93126	−	10.9396i	−0.130828	−	0.488258i
$503$	14.9589	−	4.00822i	0.666983	−	0.178718i	0.0905878	−	0.995888i	$-0.471125\pi$
$503$	14.9589	−	4.00822i	0.666983	−	0.178718i	0.576396	+	0.817171i	$0.304459\pi$
$504$	−4.14719	+	2.39438i	−0.184731	+	0.106654i
$505$	1.89912	−	9.46317i	0.0845095	−	0.421105i
$506$	28.0948	−	16.2205i	1.24896	−	0.721090i
$507$	−13.1525	−	49.0857i	−0.584122	−	2.17997i
$508$	−11.9031	+	11.9031i	−0.528114	+	0.528114i
$509$	15.7544	+	9.09580i	0.698301	+	0.403164i	0.806714	−	0.590942i	$-0.201244\pi$
$509$	15.7544	+	9.09580i	0.698301	+	0.403164i	−0.108413	+	0.994106i	$0.534577\pi$
$510$	−23.4724	−	11.6251i	−1.03938	−	0.514769i
$511$	−6.84271	−	11.8519i	−0.302704	−	0.524298i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	7.04745	+	1.88836i	0.311152	+	0.0833730i
$514$		−	26.8179i		−	1.18289i
$515$	10.0022	+	15.0247i	0.440749	+	0.662067i
$516$	−5.74750	+	12.6304i	−0.253020	+	0.556021i
$517$	−4.51529	−	4.51529i	−0.198582	−	0.198582i
$518$	−5.18428	−	5.18428i	−0.227784	−	0.227784i
$519$	24.7139	+	42.8057i	1.08482	+	1.87896i
$520$	2.67675	−	13.3381i	0.117383	−	0.584914i
$521$	4.22677	−	2.44033i	0.185178	−	0.106913i	−0.404545	−	0.914518i	$-0.632570\pi$
$521$	4.22677	−	2.44033i	0.185178	−	0.106913i	0.589723	+	0.807605i	$0.299237\pi$
$522$	−1.48462	+	5.54067i	−0.0649800	+	0.242509i
$523$	23.7706	−	6.36931i	1.03942	−	0.278511i	0.301544	−	0.953452i	$-0.402498\pi$
$523$	23.7706	−	6.36931i	1.03942	−	0.278511i	0.737871	+	0.674942i	$0.235831\pi$
$524$	5.17965			0.226274
$525$	27.2662	−	20.7748i	1.19000	−	0.906687i
$526$	−5.44255	−	9.42678i	−0.237307	−	0.411027i
$527$	32.5879	+	32.5879i	1.41955	+	1.41955i
$528$	3.05235	−	11.3915i	0.132837	−	0.495753i
$529$	9.42684	+	5.44259i	0.409863	+	0.236634i
$530$	−5.58261	+	6.34390i	−0.242493	+	0.275561i
$531$	1.98112	−	3.43140i	0.0859732	−	0.148910i
$532$	5.18988	+	5.18988i	0.225010	+	0.225010i
$533$	−0.941448	−	3.51353i	−0.0407786	−	0.152188i
$534$	−13.2802	+	23.0020i	−0.574691	+	0.995395i
$535$	37.1242	+	18.3864i	1.60502	+	0.794912i
$536$	−2.95760	+	1.70757i	−0.127749	+	0.0737559i
$537$	−5.17048	−	5.17048i	−0.223123	−	0.223123i
$538$	−1.51442	−	1.51442i	−0.0652915	−	0.0652915i
$539$	−16.8720	+	9.74103i	−0.726727	+	0.419576i
$540$	6.45317	+	3.19604i	0.277700	+	0.137536i
$541$	−1.93420	+	3.35014i	−0.0831580	+	0.144034i	−0.904605	−	0.426251i	$-0.859834\pi$
$541$	−1.93420	+	3.35014i	−0.0831580	+	0.144034i	0.821447	+	0.570285i	$0.193167\pi$
$542$	0.353186	+	1.31811i	0.0151706	+	0.0566176i
$543$	−34.3064	−	34.3064i	−1.47223	−	1.47223i
$544$	2.76777	−	4.79391i	0.118667	−	0.205537i
$545$	−19.1424	+	21.7528i	−0.819971	+	0.931789i
$546$	36.1218	+	20.8549i	1.54587	+	0.892509i
$547$	−4.57657	+	17.0800i	−0.195680	+	0.730287i	0.796410	+	0.604757i	$0.206730\pi$
$547$	−4.57657	+	17.0800i	−0.195680	+	0.730287i	−0.992090	+	0.125530i	$0.959937\pi$
$548$	1.67454	+	1.67454i	0.0715330	+	0.0715330i
$549$	−0.124871	−	0.216283i	−0.00532937	−	0.00923073i
$550$	−3.73128	+	27.6141i	−0.159102	+	1.17747i
$551$	8.79159			0.374534
$552$	11.8986	−	3.18823i	0.506440	−	0.135700i
$553$	7.56084	−	28.2175i	0.321520	−	1.19993i
$554$	−5.54402	+	3.20084i	−0.235543	+	0.135991i
$555$	2.10703	−	10.4992i	0.0894385	−	0.445666i
$556$	−4.18554	−	7.24956i	−0.177506	−	0.307450i
$557$	31.0891	+	31.0891i	1.31729	+	1.31729i	0.915915	+	0.401372i	$0.131466\pi$
$557$	31.0891	+	31.0891i	1.31729	+	1.31729i	0.401372	+	0.915915i	$0.368534\pi$
$558$	8.70189	+	8.70189i	0.368380	+	0.368380i
$559$	39.7090	−	3.84587i	1.67951	−	0.162663i
$560$	4.01441	+	6.03021i	0.169640	+	0.254823i
$561$			65.2827i			2.75624i
$562$	12.5360	+	3.35902i	0.528800	+	0.141692i
$563$	25.4934	−	25.4934i	1.07442	−	1.07442i	0.0774218	−	0.996998i	$-0.475331\pi$
$563$	25.4934	−	25.4934i	1.07442	−	1.07442i	0.996998	−	0.0774218i	$-0.0246688\pi$
$564$	−1.21235	−	2.09986i	−0.0510493	−	0.0884200i
$565$	42.3638	+	20.9814i	1.78226	+	0.882693i
$566$	−20.3993	−	11.7775i	−0.857446	−	0.495047i
$567$	−25.7707	+	25.7707i	−1.08227	+	1.08227i
$568$	−2.80524	−	10.4693i	−0.117705	−	0.439281i
$569$	2.21130	−	1.27670i	0.0927026	−	0.0535219i	−0.452932	−	0.891545i	$-0.649622\pi$
$569$	2.21130	−	1.27670i	0.0927026	−	0.0535219i	0.545635	+	0.838023i	$0.316289\pi$
$570$	−2.10931	+	10.5105i	−0.0883491	+	0.440238i
$571$	−0.574019	+	0.331410i	−0.0240219	+	0.0138691i	−0.511963	−	0.859008i	$-0.671081\pi$
$571$	−0.574019	+	0.331410i	−0.0240219	+	0.0138691i	0.487941	+	0.872877i	$0.337748\pi$
$572$	−32.7504	+	8.77543i	−1.36936	+	0.366919i
$573$	−1.47905	−	5.51988i	−0.0617881	−	0.230596i
$574$	1.67747	+	0.968490i	0.0700164	+	0.0404240i
$575$	−26.9278	+	11.0465i	−1.12297	+	0.460669i
$576$	0.739071	−	1.28011i	0.0307946	−	0.0533379i
$577$	5.38079	+	20.0814i	0.224005	+	0.835999i	0.982801	+	0.184670i	$0.0591216\pi$
$577$	5.38079	+	20.0814i	0.224005	+	0.835999i	−0.758795	+	0.651329i	$0.774212\pi$
$578$	−3.53084	+	13.1773i	−0.146864	+	0.548103i
$579$	−8.79132	−	15.2270i	−0.365355	−	0.632813i
$580$	8.50773	+	1.70737i	0.353264	+	0.0708948i
$581$			0.840151i			0.0348553i
$582$	−2.39283	+	8.93016i	−0.0991860	+	0.370167i
$583$	20.3437	+	5.45108i	0.842550	+	0.225761i
$584$	3.65832	+	2.11213i	0.151382	+	0.0874005i
$585$	1.28097	+	20.0678i	0.0529614	+	0.829703i
$586$		−	12.9676i		−	0.535685i
$587$	−3.59397	−	13.4129i	−0.148339	−	0.553609i	−0.999584	−	0.0288404i	$-0.990819\pi$
$587$	−3.59397	−	13.4129i	−0.148339	−	0.553609i	0.851245	−	0.524769i	$-0.175848\pi$
$588$	−7.14558	+	1.91465i	−0.294679	+	0.0789590i
$589$	9.43077	−	16.3346i	0.388588	−	0.673054i
$590$	−5.37123	−	2.66019i	−0.221130	−	0.109518i
$591$		−	25.8716i		−	1.06421i
$592$	2.18595	+	0.585723i	0.0898419	+	0.0240731i
$593$	4.06297	−	1.08867i	0.166846	−	0.0447063i	−0.174429	−	0.984670i	$-0.555808\pi$
$593$	4.06297	−	1.08867i	0.166846	−	0.0447063i	0.341275	+	0.939963i	$0.389141\pi$
$594$		−	17.9479i		−	0.736410i
$595$	−30.1042	−	26.4916i	−1.23415	−	1.08605i
$596$	−8.13470	+	4.69657i	−0.333210	+	0.192379i
$597$	12.3180	−	45.9715i	0.504143	−	1.88149i
$598$	−25.0422	−	25.0422i	−1.02405	−	1.02405i
$599$	−33.4777	+	19.3284i	−1.36786	+	0.789735i	−0.990655	−	0.136394i	$-0.956449\pi$
$599$	−33.4777	+	19.3284i	−1.36786	+	0.789735i	−0.377207	+	0.926129i	$0.623115\pi$
$600$	−4.08240	+	9.76153i	−0.166663	+	0.398513i
$601$			30.3653i			1.23863i	0.785144	+	0.619314i	$0.212589\pi$
$601$			30.3653i			1.23863i	−0.785144	+	0.619314i	$0.787411\pi$
$602$	−13.5039	+	16.4001i	−0.550377	+	0.668419i
$603$	3.56952	−	3.56952i	0.145362	−	0.145362i
$604$	−11.5511			−0.470008
$605$	42.4963	−	14.3448i	1.72772	−	0.583199i
$606$	−9.13428			−0.371055
$607$	13.1230	+	3.51631i	0.532647	+	0.142722i	0.515110	−	0.857124i	$-0.327751\pi$
$607$	13.1230	+	3.51631i	0.532647	+	0.142722i	0.0175369	+	0.999846i	$0.494418\pi$
$608$	−2.18831	−	0.586356i	−0.0887477	−	0.0237799i
$609$	−13.3024	+	23.0404i	−0.539039	+	0.933643i
$610$	−0.314486	+	0.209358i	−0.0127332	+	0.00847666i
$611$	−3.48548	+	6.03703i	−0.141008	+	0.244232i
$612$	−2.11774	+	7.90350i	−0.0856044	+	0.319480i
$613$	1.71656	−	1.71656i	0.0693313	−	0.0693313i	−0.671591	−	0.740922i	$-0.734389\pi$
$613$	1.71656	−	1.71656i	0.0693313	−	0.0693313i	0.740922	+	0.671591i	$0.234389\pi$
$614$	12.3930	+	21.4652i	0.500139	+	0.866266i
$615$	0.180221	+	2.82338i	0.00726722	+	0.113850i
$616$	9.02750	−	15.6361i	0.363728	−	0.629996i
$617$	−8.28504	+	2.21997i	−0.333543	+	0.0893726i	−0.421704	−	0.906734i	$-0.638568\pi$
$617$	−8.28504	+	2.21997i	−0.333543	+	0.0893726i	0.0881606	+	0.996106i	$0.471901\pi$
$618$	12.0785	−	12.0785i	0.485870	−	0.485870i
$619$	−32.4442	−	18.7316i	−1.30404	−	0.752888i	−0.322946	−	0.946417i	$-0.604673\pi$
$619$	−32.4442	−	18.7316i	−1.30404	−	0.752888i	−0.981095	+	0.193529i	$0.938007\pi$
$620$	12.2985	−	13.9757i	0.493921	−	0.561276i
$621$	16.2352	−	9.37342i	0.651498	−	0.376142i
$622$	11.8762	+	3.18222i	0.476192	+	0.127595i
$623$	−28.7527	+	28.7527i	−1.15195	+	1.15195i
$624$	−12.8745			−0.515394
$625$	6.63497	−	24.1035i	0.265399	−	0.964139i
$626$	−10.4226	−	18.0525i	−0.416572	−	0.721525i
$627$	25.8076	−	6.91512i	1.03066	−	0.276163i
$628$	2.93054	−	0.785236i	0.116941	−	0.0313343i
$629$	−12.5272			−0.499494
$630$	−8.03866	−	7.07399i	−0.320268	−	0.281835i
$631$	−17.4994	−	10.1033i	−0.696638	−	0.402204i	0.109456	−	0.993992i	$-0.465089\pi$
$631$	−17.4994	−	10.1033i	−0.696638	−	0.402204i	−0.806094	+	0.591787i	$0.798422\pi$
$632$	2.33380	+	8.70984i	0.0928334	+	0.346459i
$633$	−12.2805	−	3.29056i	−0.488108	−	0.130788i
$634$	16.3701			0.650140
$635$	−33.7306	−	16.7057i	−1.33856	−	0.662944i
$636$	6.92590	+	3.99867i	0.274630	+	0.158558i
$637$	15.0388	+	15.0388i	0.595858	+	0.595858i
$638$	−5.59743	−	20.8899i	−0.221604	−	0.827039i
$639$	8.01049	+	13.8746i	0.316890	+	0.548870i
$640$	−2.00378	−	0.992405i	−0.0792063	−	0.0392282i
$641$		−	2.76343i		−	0.109149i	−0.998510	−	0.0545745i	$-0.982620\pi$
$641$		−	2.76343i		−	0.109149i	0.998510	−	0.0545745i	$-0.0173802\pi$
$642$	10.1473	−	37.8704i	0.400484	−	1.49463i
$643$	4.90859	−	4.90859i	0.193576	−	0.193576i	−0.603663	−	0.797239i	$-0.706293\pi$
$643$	4.90859	−	4.90859i	0.193576	−	0.193576i	0.797239	+	0.603663i	$0.206293\pi$
$644$	18.8587			0.743138
$645$	−30.8693	−	3.14416i	−1.21548	−	0.123801i
$646$	12.5408			0.493410
$647$	14.7111	−	14.7111i	0.578353	−	0.578353i	−0.356096	−	0.934449i	$-0.615892\pi$
$647$	14.7111	−	14.7111i	0.578353	−	0.578353i	0.934449	+	0.356096i	$0.115892\pi$
$648$	2.91159	−	10.8662i	0.114378	−	0.426865i
$649$			14.9387i			0.586397i
$650$	30.1726	−	3.86771i	1.18347	−	0.151704i
$651$	28.5390	+	49.4310i	1.11853	+	1.93735i
$652$	3.04243	+	11.3545i	0.119151	+	0.444677i
$653$	27.8095	+	27.8095i	1.08827	+	1.08827i	0.995707	+	0.0925612i	$0.0295054\pi$
$653$	27.8095	+	27.8095i	1.08827	+	1.08827i	0.0925612	+	0.995707i	$0.470495\pi$
$654$	23.7485	+	13.7112i	0.928639	+	0.536150i
$655$	3.70422	+	10.9737i	0.144736	+	0.428778i
$656$	−0.597885			−0.0233435
$657$	−6.03129	−	1.61608i	−0.235303	−	0.0630493i
$658$	−0.960759	−	3.58560i	−0.0374543	−	0.139781i
$659$	18.5863	+	10.7308i	0.724020	+	0.418013i	0.816230	−	0.577726i	$-0.196060\pi$
$659$	18.5863	+	10.7308i	0.724020	+	0.418013i	−0.0922106	+	0.995740i	$0.529393\pi$
$660$	26.3173	−	1.67988i	1.02440	−	0.0653892i
$661$	−5.54300			−0.215598			−0.107799	−	0.994173i	$-0.534380\pi$
$661$	−5.54300			−0.215598			−0.107799	+	0.994173i	$0.534380\pi$
$662$	14.6541	−	3.92654i	0.569546	−	0.152609i
$663$	68.8390	−	18.4454i	2.67349	−	0.716358i
$664$	−0.129664	−	0.224585i	−0.00503195	−	0.00871559i
$665$	−7.28385	+	14.7069i	−0.282456	+	0.570311i
$666$	−3.34512			−0.129621
$667$	15.9732	−	15.9732i	0.618485	−	0.618485i
$668$	17.8689	+	4.78796i	0.691368	+	0.185252i
$669$	−6.32079	+	3.64931i	−0.244376	+	0.141090i
$670$	−5.73283	−	5.04487i	−0.221478	−	0.194900i
$671$	0.815448	+	0.470799i	0.0314800	+	0.0181750i
$672$	4.84776	−	4.84776i	0.187007	−	0.187007i
$673$	−2.06555	+	0.553463i	−0.0796212	+	0.0213344i	−0.298410	−	0.954438i	$-0.596456\pi$
$673$	−2.06555	+	0.553463i	−0.0796212	+	0.0213344i	0.218789	+	0.975772i	$0.429790\pi$
$674$	11.8353	−	20.4993i	0.455878	−	0.789603i
$675$	−2.15621	+	15.9575i	−0.0829925	+	0.614204i
$676$	12.0069	+	20.7966i	0.461806	+	0.799871i
$677$	11.9774	−	11.9774i	0.460328	−	0.460328i	−0.438435	−	0.898763i	$-0.644467\pi$
$677$	11.9774	−	11.9774i	0.460328	−	0.460328i	0.898763	+	0.438435i	$0.144467\pi$
$678$	11.5795	−	43.2153i	0.444708	−	1.65967i
$679$	−7.07692	+	12.2576i	−0.271587	+	0.470403i
$680$	12.1359	+	2.43548i	0.465389	+	0.0933966i
$681$	−0.199495	+	0.345535i	−0.00764466	+	0.0132409i
$682$	−44.8173	−	12.0088i	−1.71614	−	0.459839i
$683$	3.24842	+	0.870412i	0.124297	+	0.0333054i	0.320431	−	0.947272i	$-0.396172\pi$
$683$	3.24842	+	0.870412i	0.124297	+	0.0333054i	−0.196134	+	0.980577i	$0.562839\pi$
$684$	3.34874			0.128042
$685$	−2.35018	+	4.74528i	−0.0897956	+	0.181308i
$686$	11.3527			0.433447
$687$	−42.5960	+	42.5960i	−1.62514	+	1.62514i
$688$	1.07869	−	6.46811i	0.0411246	−	0.246594i
$689$		−	22.9921i		−	0.875930i
$690$	15.2640	+	22.9287i	0.581090	+	0.872880i
$691$	−5.94389	+	3.43170i	−0.226116	+	0.130548i	−0.608779	−	0.793340i	$-0.708340\pi$
$691$	−5.94389	+	3.43170i	−0.226116	+	0.130548i	0.382663	+	0.923888i	$0.375007\pi$
$692$	−16.5161	−	16.5161i	−0.627847	−	0.627847i
$693$	−6.90732	+	25.7785i	−0.262387	+	0.979243i
$694$	29.1697	−	16.8411i	1.10727	−	0.639281i
$695$	12.3658	−	14.0521i	0.469061	−	0.533026i
$696$		−	8.21205i		−	0.311277i
$697$	3.19684	−	0.856591i	0.121089	−	0.0324457i
$698$	−9.63903	−	2.58277i	−0.364843	−	0.0977593i
$699$		−	3.69362i		−	0.139706i
$700$	−9.90484	+	12.8175i	−0.374368	+	0.484457i
$701$	3.68063	−	6.37505i	0.139016	−	0.240782i	−0.788109	−	0.615536i	$-0.788940\pi$
$701$	3.68063	−	6.37505i	0.139016	−	0.240782i	0.927124	+	0.374754i	$0.122273\pi$
$702$	−18.9256	+	5.07109i	−0.714300	+	0.191396i
$703$	1.32696	+	4.95227i	0.0500472	+	0.186779i
$704$			5.57301i			0.210041i
$705$	3.58179	−	4.07024i	0.134898	−	0.153294i
$706$	20.6361	+	11.9143i	0.776650	+	0.448399i
$707$	−13.5076	−	3.61934i	−0.508004	−	0.136119i
$708$	−1.46815	+	5.47919i	−0.0551763	+	0.205921i
$709$		−	4.54637i		−	0.170742i	−0.996349	−	0.0853712i	$-0.972792\pi$
$709$		−	4.54637i		−	0.170742i	0.996349	−	0.0853712i	$-0.0272076\pi$
$710$	20.1743	−	13.4303i	0.757128	−	0.504032i
$711$	−6.66427	−	11.5429i	−0.249930	−	0.432891i
$712$	3.24850	−	12.1236i	0.121743	−	0.454350i
$713$	−12.5433	−	46.8124i	−0.469752	−	1.75314i
$714$	−18.9752	+	32.8660i	−0.710128	+	1.22998i
$715$	−42.0132	−	63.1099i	−1.57121	−	2.36018i
$716$	2.99245	+	1.72769i	0.111833	+	0.0645670i
$717$	15.3200	+	57.1749i	0.572135	+	2.13524i
$718$	−1.88587	+	0.505316i	−0.0703799	+	0.0188582i
$719$	19.5942	−	11.3127i	0.730742	−	0.421894i	−0.0879518	−	0.996125i	$-0.528032\pi$
$719$	19.5942	−	11.3127i	0.730742	−	0.421894i	0.818693	+	0.574231i	$0.194699\pi$
$720$	3.24061	+	0.650342i	0.120771	+	0.0242368i
$721$	22.6474	−	13.0755i	0.843434	−	0.486957i
$722$	3.58917	+	13.3950i	0.133575	+	0.498509i
$723$	−23.3671	+	23.3671i	−0.869030	+	0.869030i
$724$	19.8551	+	11.4633i	0.737908	+	0.426031i
$725$	2.46703	+	19.2457i	0.0916230	+	0.714767i
$726$	−21.2235	−	36.7601i	−0.787677	−	1.36430i
$727$	3.53919	−	3.53919i	0.131261	−	0.131261i	−0.638424	−	0.769685i	$-0.720413\pi$
$727$	3.53919	−	3.53919i	0.131261	−	0.131261i	0.769685	+	0.638424i	$0.220413\pi$
$728$	−19.0385	−	5.10136i	−0.705615	−	0.189069i
$729$		−	3.81690i		−	0.141367i
$730$	−1.85856	+	9.26108i	−0.0687884	+	0.342768i
$731$	3.49922	+	36.1299i	0.129423	+	1.33631i
$732$	0.252819	+	0.252819i	0.00934446	+	0.00934446i
$733$	14.2337	+	14.2337i	0.525733	+	0.525733i	0.919297	−	0.393564i	$-0.128758\pi$
$733$	14.2337	+	14.2337i	0.525733	+	0.525733i	−0.393564	+	0.919297i	$0.628758\pi$
$734$	5.88187	+	10.1877i	0.217104	+	0.376035i
$735$	−9.16659	−	13.7695i	−0.338115	−	0.507897i
$736$	−5.04122	+	2.91055i	−0.185822	+	0.107284i
$737$	−4.92601	+	18.3841i	−0.181452	+	0.677187i
$738$	0.853646	−	0.228734i	0.0314231	−	0.00841980i
$739$	−26.5396			−0.976274			−0.488137	−	0.872767i	$-0.662323\pi$
$739$	−26.5396			−0.976274			−0.488137	+	0.872767i	$0.662323\pi$
$740$	0.322356	+	5.05008i	0.0118500	+	0.185645i
$741$	−14.5836	−	25.2596i	−0.535744	−	0.927935i
$742$	8.65743	+	8.65743i	0.317824	+	0.317824i
$743$	3.16784	−	11.8225i	0.116217	−	0.433727i	−0.883158	−	0.469075i	$-0.844587\pi$
$743$	3.16784	−	11.8225i	0.116217	−	0.433727i	0.999375	+	0.0353481i	$0.0112540\pi$
$744$	−15.2578	−	8.80909i	−0.559378	−	0.322957i
$745$	−15.7678	−	13.8756i	−0.577687	−	0.508362i
$746$	−9.94459	+	17.2245i	−0.364097	+	0.630635i
$747$	0.271051	+	0.271051i	0.00991724	+	0.00991724i
$748$	−7.98446	−	29.7984i	−0.291941	−	1.08954i
$749$	30.0113	−	51.9811i	1.09659	−	1.89935i
$750$	−23.6005	−	1.66810i	−0.861770	−	0.0609106i
$751$	−41.4985	+	23.9592i	−1.51430	+	0.874282i	−0.514441	+	0.857526i	$0.672001\pi$
$751$	−41.4985	+	23.9592i	−1.51430	+	0.874282i	−0.999860	+	0.0167563i	$0.994666\pi$
$752$	0.810206	+	0.810206i	0.0295452	+	0.0295452i
$753$	−16.9470	−	16.9470i	−0.617581	−	0.617581i
$754$	−20.4463	+	11.8047i	−0.744612	+	0.429902i
$755$	−8.26078	−	24.4724i	−0.300641	−	0.890643i
$756$	5.21676	−	9.03569i	0.189732	−	0.328625i
$757$	−5.28549	−	19.7257i	−0.192104	−	0.716943i	−0.992997	−	0.118136i	$-0.962308\pi$
$757$	−5.28549	−	19.7257i	−0.192104	−	0.716943i	0.800893	−	0.598807i	$-0.204358\pi$
$758$	16.6601	+	16.6601i	0.605121	+	0.605121i
$759$	34.3252	−	59.4531i	1.24593	−	2.15801i
$760$	−0.322704	−	5.05553i	−0.0117057	−	0.183383i
$761$	−5.66635	−	3.27147i	−0.205405	−	0.118591i	0.393769	−	0.919209i	$-0.371171\pi$
$761$	−5.66635	−	3.27147i	−0.205405	−	0.118591i	−0.599174	+	0.800619i	$0.704504\pi$
$762$	−9.21976	+	34.4086i	−0.333997	+	1.24649i
$763$	29.6858	+	29.6858i	1.07470	+	1.07470i
$764$	1.35023	+	2.33866i	0.0488496	+	0.0846099i
$765$	−18.2590	+	1.16551i	−0.660157	+	0.0421390i
$766$	14.2136			0.513558
$767$	15.7525	−	4.22088i	0.568791	−	0.152407i
$768$	−0.547703	+	2.04406i	−0.0197635	+	0.0737585i
$769$	−15.1824	+	8.76554i	−0.547490	+	0.316094i	−0.748109	−	0.663576i	$-0.769038\pi$
$769$	−15.1824	+	8.76554i	−0.547490	+	0.316094i	0.200619	+	0.979669i	$0.435705\pi$
$770$	39.5830	+	7.94371i	1.42647	+	0.286271i
$771$	−28.3756	−	49.1479i	−1.02192	−	1.77002i
$772$	5.87517	+	5.87517i	0.211452	+	0.211452i
$773$	27.6211	+	27.6211i	0.993460	+	0.993460i	0.999979	−	0.00651837i	$-0.00207488\pi$
$773$	27.6211	+	27.6211i	0.993460	+	0.993460i	−0.00651837	+	0.999979i	$0.502075\pi$
$774$	0.934390	+	9.64768i	0.0335860	+	0.346779i
$775$	38.4044	+	16.0612i	1.37953	+	0.576937i
$776$		−	4.36885i		−	0.156832i
$777$	−14.9864	−	4.01558i	−0.537633	−	0.144058i
$778$	−13.0169	+	13.0169i	−0.466680	+	0.466680i
$779$	−0.677256	−	1.17304i	−0.0242652	−	0.0420286i
$780$	−9.20722	−	27.2763i	−0.329671	−	0.976647i
$781$	−52.3111	−	30.2018i	−1.87184	−	1.08071i
$782$	22.7850	−	22.7850i	0.814791	−	0.814791i
$783$	−3.23461	−	12.0717i	−0.115596	−	0.431408i
$784$	3.02744	−	1.74789i	0.108123	−	0.0624248i
$785$	3.75940	+	5.64715i	0.134179	+	0.201555i
$786$	9.49248	−	5.48048i	0.338585	−	0.195482i
$787$	−30.6835	+	8.22162i	−1.09375	+	0.293069i	−0.760217	−	0.649669i	$-0.774907\pi$
$787$	−30.6835	+	8.22162i	−1.09375	+	0.293069i	−0.333532	+	0.942739i	$0.608241\pi$
$788$	3.16424	+	11.8091i	0.112721	+	0.420682i
$789$	−19.9486	−	11.5173i	−0.710188	−	0.410027i
$790$	−16.7839	+	11.1733i	−0.597143	+	0.397527i
$791$	34.2470	−	59.3175i	1.21768	−	2.10909i
$792$	−2.13207	−	7.95701i	−0.0757599	−	0.282740i
$793$	0.266044	−	0.992892i	0.00944752	−	0.0352586i
$794$	−3.72325	−	6.44887i	−0.132133	−	0.228862i
$795$	−3.51861	+	17.5330i	−0.124792	+	0.621832i
$796$			22.4903i			0.797149i
$797$	−4.35871	+	16.2669i	−0.154394	+	0.576204i	0.844763	+	0.535141i	$0.179741\pi$
$797$	−4.35871	+	16.2669i	−0.154394	+	0.576204i	−0.999157	+	0.0410639i	$0.986925\pi$
$798$	15.0026	+	4.01992i	0.531085	+	0.142304i
$799$	−5.49289	−	3.17132i	−0.194324	−	0.112193i
$800$	0.669527	−	4.95497i	0.0236713	−	0.175185i
$801$			18.5525i			0.655520i
$802$	−0.434848	−	1.62287i	−0.0153550	−	0.0573057i
$803$	22.7397	−	6.09308i	0.802466	−	0.215020i
$804$	−3.61350	+	6.25876i	−0.127438	+	0.220730i
$805$	13.4868	+	39.9545i	0.475348	+	1.40821i
$806$			50.6518i			1.78413i
$807$	−4.37779	−	1.17303i	−0.154106	−	0.0412925i
$808$	4.16936	−	1.11718i	0.146678	−	0.0393021i
$809$		−	37.8890i		−	1.33211i	−0.745905	−	0.666053i	$-0.767983\pi$
$809$		−	37.8890i		−	1.33211i	0.745905	−	0.666053i	$-0.232017\pi$
$810$	25.1036	−	1.60241i	0.882051	−	0.0563029i
$811$	2.32747	−	1.34377i	0.0817286	−	0.0471860i	−0.458579	−	0.888654i	$-0.651641\pi$
$811$	2.32747	−	1.34377i	0.0817286	−	0.0471860i	0.540307	+	0.841468i	$0.318308\pi$
$812$	3.25392	−	12.1438i	0.114190	−	0.426163i
$813$	2.04193	+	2.04193i	0.0716137	+	0.0716137i
$814$	10.9224	−	6.30603i	0.382829	−	0.221026i
$815$	−21.8801	+	14.5659i	−0.766427	+	0.510223i
$816$		−	11.7141i		−	0.410075i
$817$	13.9122	−	5.21040i	0.486727	−	0.182289i
$818$	−3.96979	+	3.96979i	−0.138800	+	0.138800i
$819$	29.1344			1.01804
$820$	−0.427578	−	1.26669i	−0.0149317	−	0.0442348i
$821$	−42.3998			−1.47976			−0.739881	−	0.672737i	$-0.765118\pi$
$821$	−42.3998			−1.47976			−0.739881	+	0.672737i	$0.765118\pi$
$822$	4.84066	+	1.29705i	0.168837	+	0.0452398i
$823$	−20.5835	−	5.51533i	−0.717496	−	0.192252i	−0.118442	−	0.992961i	$-0.537790\pi$
$823$	−20.5835	−	5.51533i	−0.717496	−	0.192252i	−0.599054	+	0.800709i	$0.704457\pi$
$824$	−4.03599	+	6.99055i	−0.140601	+	0.243527i
$825$	22.3798	+	54.5550i	0.779166	+	1.89936i
$826$	−4.34212	+	7.52077i	−0.151082	+	0.261681i
$827$	−10.5719	+	39.4549i	−0.367621	+	1.37198i	0.496212	+	0.868202i	$0.334724\pi$
$827$	−10.5719	+	39.4549i	−0.367621	+	1.37198i	−0.863833	+	0.503779i	$0.831943\pi$
$828$	6.08424	−	6.08424i	0.211442	−	0.211442i
$829$	25.8618	+	44.7939i	0.898217	+	1.55576i	0.829772	+	0.558103i	$0.188470\pi$
$829$	25.8618	+	44.7939i	0.898217	+	1.55576i	0.0684450	+	0.997655i	$0.478196\pi$
$830$	0.383081	−	0.435321i	0.0132969	−	0.0151102i
$831$	−6.77350	+	11.7320i	−0.234970	+	0.406980i
$832$	5.87660	−	1.57463i	0.203734	−	0.0545905i
$833$	−13.6833	+	13.6833i	−0.474097	+	0.474097i
$834$	−15.3412	−	8.85727i	−0.531224	−	0.306702i
$835$	2.63508	+	41.2816i	0.0911905	+	1.42861i
$836$	−10.9342	+	6.31284i	−0.378166	+	0.218334i
$837$	−25.8988	−	6.93955i	−0.895192	−	0.239866i
$838$	−16.1587	+	16.1587i	−0.558193	+	0.558193i
$839$	−31.3971			−1.08395			−0.541974	−	0.840395i	$-0.682323\pi$
$839$	−31.3971			−1.08395			−0.541974	+	0.840395i	$0.682323\pi$
$840$	13.7375	+	6.80370i	0.473987	+	0.234750i
$841$	6.97034	+	12.0730i	0.240357	+	0.416310i
$842$	25.6191	−	6.86461i	0.882892	−	0.236570i
$843$	26.5283	−	7.10822i	0.913682	−	0.244820i
$844$	6.00793			0.206801
$845$	−35.4734	+	40.3109i	−1.22032	+	1.38674i
$846$	−1.46675	−	0.846831i	−0.0504280	−	0.0291146i
$847$	−16.8190	−	62.7695i	−0.577909	−	2.15679i
$848$	−3.65040	−	0.978121i	−0.125355	−	0.0335888i
$849$	−49.8464			−1.71072
$850$	3.51909	+	27.4530i	0.120704	+	0.941631i
$851$	11.4086	+	6.58675i	0.391081	+	0.225791i
$852$	−16.2184	−	16.2184i	−0.555632	−	0.555632i
$853$	6.48699	+	24.2098i	0.222110	+	0.828927i	0.983542	+	0.180681i	$0.0578303\pi$
$853$	6.48699	+	24.2098i	0.222110	+	0.828927i	−0.761431	+	0.648245i	$0.775503\pi$
$854$	0.273686	+	0.474039i	0.00936536	+	0.0162213i
$855$	2.39485	+	7.09471i	0.0819021	+	0.242634i
$856$			18.5271i			0.633243i
$857$	7.30272	−	27.2541i	0.249456	−	0.930983i	−0.721635	−	0.692274i	$-0.756609\pi$
$857$	7.30272	−	27.2541i	0.249456	−	0.930983i	0.971091	−	0.238709i	$-0.0767243\pi$
$858$	−50.7348	+	50.7348i	−1.73206	+	1.73206i
$859$	−20.1121			−0.686215			−0.343108	−	0.939296i	$-0.611480\pi$
$859$	−20.1121			−0.686215			−0.343108	+	0.939296i	$0.611480\pi$
$860$	14.4749	−	2.34034i	0.493590	−	0.0798049i
$861$	4.09897			0.139692
$862$	10.5781	−	10.5781i	0.360293	−	0.360293i
$863$	3.50241	−	13.0712i	0.119224	−	0.444948i	−0.880345	−	0.474335i	$-0.842689\pi$
$863$	3.50241	−	13.0712i	0.119224	−	0.444948i	0.999568	+	0.0293863i	$0.00935531\pi$
$864$			3.22050i			0.109564i
$865$	23.1799	−	46.8028i	0.788139	−	1.59134i
$866$	−6.32710	−	10.9589i	−0.215004	−	0.372397i
$867$	7.47184	+	27.8853i	0.253757	+	0.947034i
$868$	−19.0724	−	19.0724i	−0.647359	−	0.647359i
$869$	43.5198	+	25.1262i	1.47631	+	0.852347i
$870$	17.3982	−	5.87285i	0.589855	−	0.199108i
$871$	20.7774			0.704015
$872$	−12.5170	−	3.35392i	−0.423879	−	0.113578i
$873$	1.67139	+	6.23773i	0.0565681	+	0.211115i
$874$	−11.4209	−	6.59386i	−0.386318	−	0.223041i
$875$	−34.2389	−	11.8182i	−1.15749	−	0.399526i
$876$	8.93922			0.302028
$877$	−5.51197	+	1.47693i	−0.186126	+	0.0498724i	−0.350678	−	0.936496i	$-0.614049\pi$
$877$	−5.51197	+	1.47693i	−0.186126	+	0.0498724i	0.164552	+	0.986368i	$0.447382\pi$
$878$	27.0576	−	7.25007i	0.913150	−	0.244678i
$879$	−13.7207	−	23.7650i	−0.462789	−	0.801574i
$880$	−11.8071	+	3.98554i	−0.398017	+	0.134353i
$881$	26.4326			0.890538			0.445269	−	0.895397i	$-0.353108\pi$
$881$	26.4326			0.890538			0.445269	+	0.895397i	$0.353108\pi$
$882$	−3.65381	+	3.65381i	−0.123030	+	0.123030i
$883$	1.92167	+	0.514911i	0.0646694	+	0.0173281i	0.291009	−	0.956720i	$-0.406009\pi$
$883$	1.92167	+	0.514911i	0.0646694	+	0.0173281i	−0.226339	+	0.974049i	$0.572676\pi$
$884$	−29.1657	+	16.8388i	−0.980949	+	0.566351i
$885$	−12.6583	+	0.808001i	−0.425504	+	0.0271607i
$886$	28.1180	+	16.2339i	0.944641	+	0.545389i
$887$	1.11901	−	1.11901i	0.0375726	−	0.0375726i	−0.688071	−	0.725643i	$-0.741542\pi$
$887$	1.11901	−	1.11901i	0.0375726	−	0.0375726i	0.725643	+	0.688071i	$0.241542\pi$
$888$	4.62582	−	1.23948i	0.155232	−	0.0415944i
$889$	−27.2679	+	47.2294i	−0.914537	+	1.58402i
$890$	28.0084	−	1.78783i	0.938844	−	0.0599281i
$891$	−31.3469	−	54.2943i	−1.05016	−	1.81893i
$892$	2.43880	−	2.43880i	0.0816571	−	0.0816571i
$893$	−0.671849	+	2.50737i	−0.0224826	+	0.0839061i
$894$	−9.93870	+	17.2143i	−0.332400	+	0.575734i
$895$	−1.52028	+	7.57544i	−0.0508172	+	0.253219i
$896$	−1.61986	+	2.80568i	−0.0541157	+	0.0937312i
$897$	−72.3902	−	19.3969i	−2.41704	−	0.647644i
$898$	1.29551	+	0.347131i	0.0432318	+	0.0115839i
$899$	−32.3084			−1.07754
$900$	0.939696	+	7.33073i	0.0313232	+	0.244358i
$901$	20.9197			0.696937
$902$	−2.35609	+	2.35609i	−0.0784494	+	0.0784494i
$903$	−7.39523	+	44.3439i	−0.246098	+	1.47567i
$904$			21.1419i			0.703171i
$905$	−10.0871	+	50.2634i	−0.335307	+	1.67081i
$906$	−21.1691	+	12.2220i	−0.703298	+	0.406049i
$907$	34.5466	+	34.5466i	1.14710	+	1.14710i	0.987120	+	0.159981i	$0.0511433\pi$
$907$	34.5466	+	34.5466i	1.14710	+	1.14710i	0.159981	+	0.987120i	$0.448857\pi$
$908$	0.0487988	−	0.182120i	0.00161945	−	0.00604385i
$909$	−5.52551	+	3.19015i	−0.183270	+	0.105811i
$910$	−2.80756	−	43.9837i	−0.0930697	−	1.45805i
$911$		−	36.6230i		−	1.21337i	−0.794941	−	0.606686i	$-0.792498\pi$
$911$		−	36.6230i		−	1.21337i	0.794941	−	0.606686i	$-0.207502\pi$
$912$	−4.63082	+	1.24082i	−0.153342	+	0.0410878i
$913$	−1.39599	−	0.374056i	−0.0462007	−	0.0123794i
$914$		−	21.9727i		−	0.726791i
$915$	−0.354824	+	0.716431i	−0.0117301	+	0.0236845i
$916$	14.2333	−	24.6528i	0.470281	−	0.814551i
$917$	16.2088	−	4.34314i	0.535262	−	0.143423i
$918$	−4.61401	−	17.2197i	−0.152285	−	0.568336i
$919$			48.0128i			1.58380i	0.610654	+	0.791898i	$0.290907\pi$
$919$			48.0128i			1.58380i	−0.610654	+	0.791898i	$0.709093\pi$
$920$	−9.77158	−	8.59896i	−0.322160	−	0.283499i
$921$	45.4239	+	26.2255i	1.49677	+	0.864160i
$922$	3.50508	+	0.939184i	0.115434	+	0.0309304i
$923$	−17.0668	+	63.6941i	−0.561760	+	2.09652i
$924$		−	38.2073i		−	1.25693i
$925$	−10.4687	+	4.29451i	−0.344208	+	0.141203i
$926$	6.59748	+	11.4272i	0.216807	+	0.375520i
$927$	3.08811	−	11.5250i	0.101427	−	0.378530i
$928$	1.00438	+	3.74840i	0.0329704	+	0.123047i
$929$	8.04900	−	13.9413i	0.264079	−	0.457399i	−0.703243	−	0.710950i	$-0.748265\pi$
$929$	8.04900	−	13.9413i	0.264079	−	0.457399i	0.967322	+	0.253551i	$0.0815986\pi$
$930$	7.75152	−	38.6253i	0.254182	−	1.26657i
$931$	6.85868	+	3.95986i	0.224784	+	0.129779i
$932$	0.451751	+	1.68596i	0.0147976	+	0.0552254i
$933$	25.1319	−	6.73408i	0.822783	−	0.220464i
$934$	−19.1624	+	11.0634i	−0.627013	+	0.362006i
$935$	57.4215	−	38.2264i	1.87788	−	1.25014i
$936$	−7.78806	+	4.49644i	−0.254561	+	0.146971i
$937$	−6.37857	−	23.8051i	−0.208379	−	0.777680i	−0.988393	−	0.151918i	$-0.951455\pi$
$937$	−6.37857	−	23.8051i	−0.208379	−	0.777680i	0.780014	−	0.625762i	$-0.215212\pi$
$938$	−7.82351	+	7.82351i	−0.255447	+	0.255447i
$939$	−38.2021	−	22.0560i	−1.24668	−	0.719770i
$940$	−1.13710	+	2.29594i	−0.0370882	+	0.0748853i
$941$	12.4961	+	21.6438i	0.407360	+	0.705568i	0.994593	−	0.103850i	$-0.0331162\pi$
$941$	12.4961	+	21.6438i	0.407360	+	0.705568i	−0.587233	+	0.809418i	$0.699783\pi$
$942$	4.53982	−	4.53982i	0.147915	−	0.147915i
$943$	−3.36176	−	0.900780i	−0.109474	−	0.0293334i
$944$		−	2.68055i		−	0.0872445i
$945$	22.8740	+	4.59046i	0.744090	+	0.149328i
$946$	−21.2382	−	29.7398i	−0.690512	−	0.966923i
$947$	15.9860	+	15.9860i	0.519474	+	0.519474i	0.917412	−	0.397938i	$-0.130274\pi$
$947$	15.9860	+	15.9860i	0.519474	+	0.519474i	−0.397938	+	0.917412i	$0.630274\pi$
$948$	13.4928	+	13.4928i	0.438224	+	0.438224i
$949$	−12.8500	−	22.2568i	−0.417128	−	0.722488i
$950$	10.4800	−	4.29915i	0.340016	−	0.139483i
$951$	30.0007	−	17.3209i	0.972838	−	0.561668i
$952$	4.64155	−	17.3225i	0.150434	−	0.561426i
$953$	−45.7568	+	12.2605i	−1.48221	+	0.397157i	−0.907098	−	0.420919i	$-0.861708\pi$
$953$	−45.7568	+	12.2605i	−1.48221	+	0.397157i	−0.575111	+	0.818075i	$0.695041\pi$
$954$	5.58615			0.180858
$955$	−3.98913	+	4.53312i	−0.129085	+	0.146688i
$956$	−13.9857	−	24.2239i	−0.452328	−	0.783456i
$957$	−32.3613	−	32.3613i	−1.04609	−	1.04609i
$958$	−4.63075	+	17.2822i	−0.149613	+	0.558363i
$959$	6.64431	+	3.83609i	0.214556	+	0.123874i
$960$	−4.72227	+	0.301431i	−0.152411	+	0.00972865i
$961$	−19.1573	+	33.1814i	−0.617977	+	1.07037i
$962$	−9.73561	−	9.73561i	−0.313889	−	0.313889i
$963$	−7.08793	−	26.4525i	−0.228405	−	0.852420i
$964$	7.80800	−	13.5239i	0.251479	−	0.435574i
$965$	−8.24563	+	16.6489i	−0.265436	+	0.535947i
$966$	34.5614	−	19.9541i	1.11200	−	0.642011i
$967$	−34.3761	−	34.3761i	−1.10546	−	1.10546i	−0.993740	−	0.111722i	$-0.964364\pi$
$967$	−34.3761	−	34.3761i	−1.10546	−	1.10546i	−0.111722	−	0.993740i	$-0.535636\pi$
$968$	14.1835	+	14.1835i	0.455874	+	0.455874i
$969$	22.9829	−	13.2692i	0.738316	−	0.426267i
$970$	9.25593	−	3.12438i	0.297190	−	0.100318i
$971$	4.17462	−	7.23065i	0.133970	−	0.232043i	−0.791234	−	0.611514i	$-0.790561\pi$
$971$	4.17462	−	7.23065i	0.133970	−	0.232043i	0.925203	+	0.379471i	$0.123894\pi$
$972$	−3.66082	−	13.6624i	−0.117421	−	0.438220i
$973$	−19.1767	−	19.1767i	−0.614776	−	0.614776i
$974$	−10.4673	+	18.1299i	−0.335394	+	0.580920i
$975$	51.2035	−	39.0132i	1.63983	−	1.24942i
$976$	−0.146321	−	0.0844784i	−0.00468362	−	0.00270409i
$977$	14.3402	−	53.5183i	0.458783	−	1.71220i	−0.217937	−	0.975963i	$-0.569933\pi$
$977$	14.3402	−	53.5183i	0.458783	−	1.71220i	0.676721	−	0.736240i	$-0.263400\pi$
$978$	17.5897	+	17.5897i	0.562457	+	0.562457i
$979$	−34.9741	−	60.5769i	−1.11778	−	1.93605i
$980$	5.86820	+	5.16400i	0.187453	+	0.164958i
$981$	19.1546			0.611558
$982$	−8.77599	+	2.35152i	−0.280053	+	0.0750400i
$983$	−5.52080	+	20.6039i	−0.176086	+	0.657163i	0.820278	+	0.571965i	$0.193819\pi$
$983$	−5.52080	+	20.6039i	−0.176086	+	0.657163i	−0.996364	+	0.0851974i	$0.972848\pi$
$984$	−1.09571	+	0.632611i	−0.0349301	+	0.0201669i
$985$	−22.7561	+	15.1491i	−0.725071	+	0.482691i
$986$	−10.7407	−	18.6034i	−0.342053	−	0.592453i
$987$	−5.55459	−	5.55459i	−0.176805	−	0.176805i
$988$	9.74613	+	9.74613i	0.310066	+	0.310066i
$989$	15.8101	−	34.7434i	0.502732	−	1.10478i
$990$	15.3331	−	10.2075i	0.487319	−	0.324416i
$991$		−	24.3127i		−	0.772319i	−0.922432	−	0.386159i	$-0.873801\pi$
$991$		−	24.3127i		−	0.772319i	0.922432	−	0.386159i	$-0.126199\pi$
$992$	8.04185	+	2.15481i	0.255329	+	0.0684152i
$993$	22.7012	−	22.7012i	0.720400	−	0.720400i
$994$	−17.5570	−	30.4096i	−0.556875	−	0.964535i
$995$	−47.6485	+	16.0840i	−1.51056	+	0.509896i
$996$	−0.475258	−	0.274390i	−0.0150591	−	0.00869439i
$997$	−33.8247	+	33.8247i	−1.07124	+	1.07124i	−0.0739797	+	0.997260i	$0.523570\pi$
$997$	−33.8247	+	33.8247i	−1.07124	+	1.07124i	−0.997260	+	0.0739797i	$0.976430\pi$
$998$	−5.40669	−	20.1780i	−0.171146	−	0.638725i
$999$	6.31175	−	3.64409i	0.199695	−	0.115294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.l.a.7.2	✓	88
5.3	odd	4	inner	430.2.l.a.93.13	yes	88
43.37	odd	6	inner	430.2.l.a.37.13	yes	88
215.123	even	12	inner	430.2.l.a.123.2	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.l.a.7.2	✓	88	1.1	even	1	trivial
430.2.l.a.37.13	yes	88	43.37	odd	6	inner
430.2.l.a.93.13	yes	88	5.3	odd	4	inner
430.2.l.a.123.2	yes	88	215.123	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.547703 + 2.04406i) q^{3} -1.00000i q^{4} +(2.11862 - 0.715150i) q^{5} +(-1.05808 - 1.83265i) q^{6} +(-0.838501 - 3.12933i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.28011 - 0.739071i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.547703 + 2.04406i) q^{3} -1.00000i q^{4} +(2.11862 - 0.715150i) q^{5} +(-1.05808 - 1.83265i) q^{6} +(-0.838501 - 3.12933i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.28011 - 0.739071i) q^{9} +(-0.992405 + 2.00378i) q^{10} +5.57301 q^{11} +(2.04406 + 0.547703i) q^{12} +(-1.57463 - 5.87660i) q^{13} +(2.80568 + 1.61986i) q^{14} +(0.301431 + 4.72227i) q^{15} -1.00000 q^{16} +(5.34691 - 1.43270i) q^{17} +(1.42778 - 0.382571i) q^{18} +(-1.13275 - 1.96198i) q^{19} +(-0.715150 - 2.11862i) q^{20} +6.85577 q^{21} +(-3.94071 + 3.94071i) q^{22} +(-5.62275 - 1.50661i) q^{23} +(-1.83265 + 1.05808i) q^{24} +(3.97712 - 3.03027i) q^{25} +(5.26882 + 3.04195i) q^{26} +(-2.27724 + 2.27724i) q^{27} +(-3.12933 + 0.838501i) q^{28} +(-1.94032 + 3.36073i) q^{29} +(-3.55229 - 3.12601i) q^{30} +(4.16277 + 7.21013i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.05235 + 11.3915i) q^{33} +(-2.76777 + 4.79391i) q^{34} +(-4.01441 - 6.03021i) q^{35} +(-0.739071 + 1.28011i) q^{36} +(-2.18595 - 0.585723i) q^{37} +(2.18831 + 0.586356i) q^{38} +12.8745 q^{39} +(2.00378 + 0.992405i) q^{40} +0.597885 q^{41} +(-4.84776 + 4.84776i) q^{42} +(-1.07869 + 6.46811i) q^{43} -5.57301i q^{44} +(-3.24061 - 0.650342i) q^{45} +(5.04122 - 2.91055i) q^{46} +(-0.810206 - 0.810206i) q^{47} +(0.547703 - 2.04406i) q^{48} +(-3.02744 + 1.74789i) q^{49} +(-0.669527 + 4.95497i) q^{50} +11.7141i q^{51} +(-5.87660 + 1.57463i) q^{52} +(3.65040 + 0.978121i) q^{53} -3.22050i q^{54} +(11.8071 - 3.98554i) q^{55} +(1.61986 - 2.80568i) q^{56} +(4.63082 - 1.24082i) q^{57} +(-1.00438 - 3.74840i) q^{58} +2.68055i q^{59} +(4.72227 - 0.301431i) q^{60} +(0.146321 + 0.0844784i) q^{61} +(-8.04185 - 2.15481i) q^{62} +(-1.23942 + 4.62559i) q^{63} +1.00000i q^{64} +(-7.53870 - 11.3242i) q^{65} +(-5.89670 - 10.2134i) q^{66} +(-0.883904 + 3.29877i) q^{67} +(-1.43270 - 5.34691i) q^{68} +(6.15919 - 10.6680i) q^{69} +(7.10262 + 1.42539i) q^{70} +(-9.38650 - 5.41930i) q^{71} +(-0.382571 - 1.42778i) q^{72} +(4.08032 - 1.09332i) q^{73} +(1.95987 - 1.13153i) q^{74} +(4.01575 + 9.78914i) q^{75} +(-1.96198 + 1.13275i) q^{76} +(-4.67298 - 17.4398i) q^{77} +(-9.10367 + 9.10367i) q^{78} +(7.80903 + 4.50855i) q^{79} +(-2.11862 + 0.715150i) q^{80} +(-5.62476 - 9.74237i) q^{81} +(-0.422769 + 0.422769i) q^{82} +(-0.250492 - 0.0671191i) q^{83} -6.85577i q^{84} +(10.3035 - 6.85920i) q^{85} +(-3.81090 - 5.33639i) q^{86} +(-5.80679 - 5.80679i) q^{87} +(3.94071 + 3.94071i) q^{88} +(-6.27562 - 10.8697i) q^{89} +(2.75132 - 1.83160i) q^{90} +(-17.0695 + 9.85507i) q^{91} +(-1.50661 + 5.62275i) q^{92} +(-17.0179 + 4.55992i) q^{93} +1.14580 q^{94} +(-3.80299 - 3.34662i) q^{95} +(1.05808 + 1.83265i) q^{96} +(-3.08924 - 3.08924i) q^{97} +(0.904776 - 3.37667i) q^{98} +(-7.13406 - 4.11885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) \) 88 * q + 4 * q^6 + 12 * q^7	\( 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) \) 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

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